subject:(Noncommutative algebra)

University of North Texas

1. Uhl, Christine. Quantum Drinfeld Hecke Algebras.

Degree: 2016, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc862764/

► Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum… (more)

Subjects/Keywords: algebra; noncommutative; Mathematics

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APA (6^th Edition):

Uhl, C. (2016). Quantum Drinfeld Hecke Algebras. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc862764/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Uhl, Christine. “Quantum Drinfeld Hecke Algebras.” 2016. Thesis, University of North Texas. Accessed January 24, 2021. https://digital.library.unt.edu/ark:/67531/metadc862764/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Uhl, Christine. “Quantum Drinfeld Hecke Algebras.” 2016. Web. 24 Jan 2021.

Vancouver:

Uhl C. Quantum Drinfeld Hecke Algebras. [Internet] [Thesis]. University of North Texas; 2016. [cited 2021 Jan 24]. Available from: https://digital.library.unt.edu/ark:/67531/metadc862764/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Uhl C. Quantum Drinfeld Hecke Algebras. [Thesis]. University of North Texas; 2016. Available from: https://digital.library.unt.edu/ark:/67531/metadc862764/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Edinburgh

2. Campbell, Chris John Montgomery. Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4.

Degree: PhD, 2016, University of Edinburgh

URL: http://hdl.handle.net/1842/22886

► Let K be the field of complex numbers. In this thesis we construct new examples of noncommutative surfaces of GK-dimension 4 using the language of… (more)

▼ Let K be the field of complex numbers. In this thesis we construct new examples of noncommutative surfaces of GK-dimension 4 using the language of formal and infinitesimal deformations as introduced by Gerstenhaber. Our approach is to find families of deformations of a certain well known GK-dimension 4 birationally commutative surface defined by Zhang and Smith in unpublished work cited in [YZ06], which we call A. Let B* and K* be respectively the bar and Koszul complexes of a PBW algebra C = KhV / (R) . We construct a graph whose vertices are elements of the free algebra KhV i and edges are relations in R. We define a map m2 : B2 ! K2 that extends to a chain map m* : B* → K*. This map allows the Gerstenhaber bracket structure to be transferred from the bar complex to the Koszul complex. In particular, m2 provides a mechanism for algorithmically determining the set of infinitesimal deformations with vanishing primary obstruction. Using the computer algebra package 'Sage' [Dev15] and a Python package developed by the author [Cam], we calculate the degree 2 component of the second Hochschild cohomology of A. Furthermore, using the map m2 we describe the variety U ⊆ HH2/2 (A) of infinitesimal deformations with vanishing primary obstruction. We further show that U decomposes as a union of 3 irreducible subvarieties Vg, Vq and Vu. More generally, let C be a Koszul algebra with relations R, and let E be a localisation of C at some (left and right) Ore set. Since R is homogeneous in degree two, there is an embedding R ,↪ C⊗C and in the following we identify R with its (nonzero) image under this map. We construct an injective linear map ~⋀ : HH²(C) → HH²(E) and prove that if f ∈ HH²(E) satisfies f(R) ⊆ C then f ∈ Im(~⋀). In this way we describe a relationship between infinitesimal deformations of C with those of E. Rogalski and Sierra [RS12] have previously examined a family of deformations of A arising from automorphism of the surface P1 X P1. By applying our understanding of the map ~⋀ we show that these deformations correspond to the variety of infinitesimal deformations Vg. Furthermore, we show that deformations defined similarly by automorphisms of other minimal rational surfaces also correspond to infinitesimal deformations lying in Vg. We introduce a new family of deformations of A, which we call Aq. We show that elements of this family have families of deformations arising from certain quantum analogues of geometric automorphisms of minimal rational surfaces, as defined by Alev and Dumas. Furthermore, we show that after taking the semi-classical limit q → 1 we obtain a family of deformations of A whose infinitesimal deformation lies in Vq. Finally, we apply a heuristic search method in the space of Hochschild 2-cocycles of A. This search yields another new family of deformations of A. We show that elements of this family are non-noetherian PBW noncommutative surfaces with GK-dimension 4. We further show that elements of this family can have as function skew field the division ring of the quantum plane Kq(u; v), the…

Subjects/Keywords: 512; deformation theory; noncommutative algebra

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APA (6^th Edition):

Campbell, C. J. M. (2016). Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/22886

Chicago Manual of Style (16^th Edition):

Campbell, Chris John Montgomery. “Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4.” 2016. Doctoral Dissertation, University of Edinburgh. Accessed January 24, 2021. http://hdl.handle.net/1842/22886.

MLA Handbook (7^th Edition):

Campbell, Chris John Montgomery. “Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4.” 2016. Web. 24 Jan 2021.

Vancouver:

Campbell CJM. Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4. [Internet] [Doctoral dissertation]. University of Edinburgh; 2016. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1842/22886.

Council of Science Editors:

Campbell CJM. Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4. [Doctoral Dissertation]. University of Edinburgh; 2016. Available from: http://hdl.handle.net/1842/22886

University of Texas – Austin

3. Orem, Hendrik Nikolas. Coordinate systems and associative algebras.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/31505

► This dissertation applies and extends the techniques of formal algebraic geometry in the setting of certain "smooth" associative algebras and their globalizations, noncommutative manifolds, roughly… (more)

▼ This dissertation applies and extends the techniques of formal algebraic geometry in the setting of certain "smooth" associative algebras and their globalizations, noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a principal bundle for an appropriate group of local coordinate changes. These bundles are shown to carry a natural flat connection with properties analogous to the classical Gelfand-Kazhdan structure. Every noncommutative manifold has an underlying smooth variety given by abelianization. A basic question is existence and uniqueness of noncommu- tative thickenings of a smooth variety, i.e., finding noncommutative manifolds abelianizing to a given smooth variety. We obtain new results in this direction by showing that noncommutative coordinate systems always arise as reductions of structure group of the commutative bundle of coordinate systems on the underlying smooth variety; this also explains a relationship between D-modules on the commutative variety and sheaves of modules for the noncommutative structure sheaf. The lower central series invariants M[subscript k] of an associative algebra A are the two-sided ideals generated by k-fold nested commutators; the M[subscript k] give a decreasing filtration of A. We study the relationship between the geometry of X = Spec A[subscript ab] and the associated graded components N[subscript k] of this filtration. We show that the N[subscript k] form coherent sheaves on a certain nilpotent thickening of X, and that Zariski localization on X coincides with noncommutative localization of A. We then construct the N[subscript k] in terms of the bundle of coordinate systems on X and the N[subscript k] invariants for the free associative algebra; in particular, since this is independent of A, we exhibit the N[subscript k] as natural vector bundles on the category of smooth schemes. Advisors/Committee Members: Ben-Zvi, David, 1974- (advisor), Freed, Daniel (committee member), Hadani, Ronny (committee member), Nadler, David (committee member), Nevins, Thomas (committee member), Schedler, Travis (committee member).

Subjects/Keywords: Noncommutative algebra; Algebraic geometry

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APA (6^th Edition):

Orem, H. N. (2015). Coordinate systems and associative algebras. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31505

Chicago Manual of Style (16^th Edition):

Orem, Hendrik Nikolas. “Coordinate systems and associative algebras.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed January 24, 2021. http://hdl.handle.net/2152/31505.

MLA Handbook (7^th Edition):

Orem, Hendrik Nikolas. “Coordinate systems and associative algebras.” 2015. Web. 24 Jan 2021.

Vancouver:

Orem HN. Coordinate systems and associative algebras. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/2152/31505.

Council of Science Editors:

Orem HN. Coordinate systems and associative algebras. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31505

Universidade Estadual de Campinas

4. Marcelo Fidelis. Identidades polinomiais em algebras T-primas.

Degree: Instituto de Matematica, Estatistica e Computação Cientifica, 2005, Universidade Estadual de Campinas

URL: http://libdigi.unicamp.br/document/?code=vtls000348409

►

In this work we study tensor products of T-prime T-ideals over infinite fields. The behaviour of these tensor products over a field of characteristic zero… (more)

▼

In this work we study tensor products of T-prime T-ideals over infinite fields. The behaviour of these tensor products over a field of characteristic zero was described by Kemer. First we show, using methods due to Regev, that such a description holds if one restricts oneself to multilinear polynomials only. Second, applying graded polynomial identities, we prove that the Tensor Product Theorem fails for the T-ideals of the algebras M1,1(E) and E E where E is the infinite dimensional Grassmann algebra; M1,1(E) consists of the 2×2 matrices over E having even (i.e. central) elements of E in the main diagonal, and the other diagonal consisting of odd (anticommuting) elements of E. Then we pass to other tensor products and study the respective graded identities. We obtain new proofs of some cases of Kemer s Tensor Product Theorem. Note that these proofs do not depend on the structure theory of T-ideals but are "elementary" ones. Finally, using graded polynomial identities once again, we show that the Tensor Product Theorem fails in one more case when the base field is of positive characteristic. All this comes to show once more that the structure theory of T-ideals is essentially about the multilinear polynomial identities

Neste trabalho estudamos os produtos tensoriais de T-ideais T-primos sobre corpos infinitos. O comportamento destes produtos tensoriais sobre corpos de caracteristica zero foi descrito por Kemer. Primeiramente mostramos, usando os m´etodos introduzidos por Regev, que tal descri¸cao vale se nos restringirmos apenas aos polinomios multilineares. Num segundo momento, aplicando identidades graduadas, mostramos que o Teorema sobre o Produto Tensorial ´e falso para os T-ideais das ´algebras M1,1(E) e E E, onde E ´e a ´algebra de Grassmann com dimensao infinita; M1,1(E) consiste das matrizes 2 × 2 sobre E tendo somente elementos pares (i.e. centrais) de E na diagonal principal, e a outra diagonal consistindo de elementos ´impares (anticomutitativos) de E. Entao voltamos nossa atencao para outros produtos tensoriais e estudamos suas respectivas identidades graduadas. Obtivemos novas demonstracoes de alguns dos casos do Teorema sobre o Produto Tensorial de Kemer. Note que estas demonstracoes nao dependem da teoria sobre a estrutura dos T-ideais, mas sao "elementares". Finalmente, usando outra vez identidades polinomiais graduadas, mostramos que o Teorema sobre o Produto Tensorial nao ´e valido em mais um caso: quando o corpo base possui caracteristica positiva. Isto vem para mostrar novamente que a teoria sobre a estrutura dos T-ideais e, essencialmente, uma teoria sobre identidades polinomiais multilineares.

Advisors/Committee Members: Guilherme Augusto de la Rocque Leal, Vyacheslav Futorny, Plamen Emilov Koshlukov, Ivan Chestakov, Antonio Jose Engler.

Subjects/Keywords: Polinomios; Polynomials; Aneis (Algebra); Noncommutative algebra; Rings (Algebra); Algebra não-comutativa

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APA (6^th Edition):

Fidelis, M. (2005). Identidades polinomiais em algebras T-primas. (Thesis). Universidade Estadual de Campinas. Retrieved from http://libdigi.unicamp.br/document/?code=vtls000348409

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Fidelis, Marcelo. “Identidades polinomiais em algebras T-primas.” 2005. Thesis, Universidade Estadual de Campinas. Accessed January 24, 2021. http://libdigi.unicamp.br/document/?code=vtls000348409.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Fidelis, Marcelo. “Identidades polinomiais em algebras T-primas.” 2005. Web. 24 Jan 2021.

Vancouver:

Fidelis M. Identidades polinomiais em algebras T-primas. [Internet] [Thesis]. Universidade Estadual de Campinas; 2005. [cited 2021 Jan 24]. Available from: http://libdigi.unicamp.br/document/?code=vtls000348409.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fidelis M. Identidades polinomiais em algebras T-primas. [Thesis]. Universidade Estadual de Campinas; 2005. Available from: http://libdigi.unicamp.br/document/?code=vtls000348409

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

5. Do, Hanh Duc. MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY.

Degree: Mathematics, 2013, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/39b741zt

► In the thesis, we initial first steps in understanding Quantum Mirror Symmetry and noncommutative compactification of moduli spaces of tori. To obtain a global invariant… (more)

▼ In the thesis, we initial first steps in understanding Quantum Mirror Symmetry and noncommutative compactification of moduli spaces of tori. To obtain a global invariant of noncommutative torus bundle, we study the monodromy of Gauss-Manin connection on periodic cyclic homology groups of Heisenberg group. Then the global monodromy map is developed, and provides a important criterion to detect when a noncommutative torus bundle is dequantizable. A process to construct the dequantizing Poisson manifold is given, when the dequantization criterion is satisfied. Naively, it seems that the Morita theory for noncommutative torus bundles can be developed naturally as in Rieffel theory for rotation algebras. However, this assumption turns out to be wrong; the Morita class of a non-dequantizable noncommutative torus bundle is not a classical object in the category of C*- algebras, and we call them C*- stacks. Even with the extended notion of C*- stacks, the Morita theory is still incompatible with noncommutative torus bundles with the infinite Poisson limit. There is no rotation algebra that can be used to compactify the moduli space of rotation algebras, even though we know that the "infinite Poisson rotation algebra" is strongly Morita equivalent to the classical torus. This subtlety is completely solved by a new mathematical structure hidden behind the quantization of constant Dirac structures on the tori.We develop a new theory of quantum spaces called spatial structure to give a better understanding of quantum spaces and torus fibrations. We clarify some examples of spatial algebras and develop a rigorous way to construct a monoidal structure from the spatial structure. Using Hilsum-Skandalis maps between groupoids, we find that a groupoid presentation of a C* - algebra implies a monoidal structure on the category of representations. We decompose the spatial product of the cyclic modules over the rotation algebras as an example, and propose a conjecture that a quantum mirror symmetry lies behind the spatial structure and the Hopfish structure in the sense of Tang and Weinstein.

Subjects/Keywords: Mathematics; bundle; C*-algebra; noncommutative geometry; noncommutative tori; Poisson geometry; quantization

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APA (6^th Edition):

Do, H. D. (2013). MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/39b741zt

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Do, Hanh Duc. “MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY.” 2013. Thesis, University of California – Berkeley. Accessed January 24, 2021. http://www.escholarship.org/uc/item/39b741zt.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Do, Hanh Duc. “MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY.” 2013. Web. 24 Jan 2021.

Vancouver:

Do HD. MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2021 Jan 24]. Available from: http://www.escholarship.org/uc/item/39b741zt.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Do HD. MONOIDAL STRUCTURE IN MIRROR SYMMETRY AND NONCOMMUTATIVE GEOMETRY. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/39b741zt

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Lund

6. Richter, Johan. Algebraic Properties of Ore Extensions and Their Commutative Subrings.

Degree: 2014, University of Lund

URL: https://lup.lub.lu.se/record/4616248 ; https://portal.research.lu.se/ws/files/6024038/4616258.pdf

► This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described as a noncommutative ring of polynomials in… (more)

Subjects/Keywords: Mathematics; Ore extension; Noncommutative algebra; Algebraic dependence

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Richter, J. (2014). Algebraic Properties of Ore Extensions and Their Commutative Subrings. (Doctoral Dissertation). University of Lund. Retrieved from https://lup.lub.lu.se/record/4616248 ; https://portal.research.lu.se/ws/files/6024038/4616258.pdf

Chicago Manual of Style (16^th Edition):

Richter, Johan. “Algebraic Properties of Ore Extensions and Their Commutative Subrings.” 2014. Doctoral Dissertation, University of Lund. Accessed January 24, 2021. https://lup.lub.lu.se/record/4616248 ; https://portal.research.lu.se/ws/files/6024038/4616258.pdf.

MLA Handbook (7^th Edition):

Richter, Johan. “Algebraic Properties of Ore Extensions and Their Commutative Subrings.” 2014. Web. 24 Jan 2021.

Vancouver:

Richter J. Algebraic Properties of Ore Extensions and Their Commutative Subrings. [Internet] [Doctoral dissertation]. University of Lund; 2014. [cited 2021 Jan 24]. Available from: https://lup.lub.lu.se/record/4616248 ; https://portal.research.lu.se/ws/files/6024038/4616258.pdf.

Council of Science Editors:

Richter J. Algebraic Properties of Ore Extensions and Their Commutative Subrings. [Doctoral Dissertation]. University of Lund; 2014. Available from: https://lup.lub.lu.se/record/4616248 ; https://portal.research.lu.se/ws/files/6024038/4616258.pdf

University of Michigan

7. Walton, Chelsea M. On Degenerations and Deformations of Sklyanin Algebras.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/86397

► A subfield of noncommutative algebra, entitled noncommutative projective algebraic geometry, was launched in the 1980s through Michael Artin, John Tate, William Schelter, and Michel van… (more)

▼ A subfield of noncommutative algebra, entitled noncommutative projective algebraic geometry, was launched in the 1980s through Michael Artin, John Tate, William Schelter, and Michel van den Bergh's classification of noncommutative projective spaces. The toughest challenge was the investigation of three-dimensional Sklyanin algebras, denoted Skly3. The ring-theoretic and homological behavior of Skly3 could not be determined using purely algebraic techniques and the geometry of smooth projective curves was surprisingly used to achieve the desired classification results. In this dissertation, we employ variants of Skly3 to broaden both the class of noncommutative algebras and the type of geometric data featured in the theory of this rapidly expanding field. Traditional techniques of this area study noncommutative graded algebras with use of projective geometric data of finite type. Even so, our research objectives include: (1) the analysis of degenerate three-dimensional Sklyanin algebras, S(deg), which are associated to geometric data not of finite type, and; (2) the study of the representation theory of ungraded deformations, S(def), of Skly3. We have completed problem (1), details of which are provided in Chapter 3 of this dissertation. Namely, we conclude that the geometry of S(deg) yields an analogue to a result of Artin-Tate-van den Bergh, namely that a generalized twisted homogeneous coordinate ring arises as a factor of S(deg). This has resulted in several open problems regarding noncommutative graded rings and corresponding noncommutative coordinate rings; such further directions are also discussed in Chapter 3. We only give a partial answer to problem (2), yet this is still sufficient as the work has several consequences not only for the advancement of the representation theory of noncommutative algebras, but also for Berenstein et al.'s study of noncommutative vacua in string theory. In particular, we present results on the dimensions of (not necessarily graded) simple finite-dimensional modules of Skly3 in Chapter 4. We also analyze the representation theory of a central extension D of Skly3 in Chapter 5 by investigating the existence of fat point modules over D and the structure of the center of D. This is all with a view towards understanding the irreducible finite-dimensional representations of S(def). Advisors/Committee Members: Smith, Karen E. (committee member), Stafford, J. Tobias (committee member), Derksen, Hendrikus Gerardus (committee member), Hochster, Melvin (committee member), Pando Zayas, Leopoldo A. (committee member).

Subjects/Keywords: Noncommutative Algebra; Noncommutative Algebraic Geometry; Representation Theory; Sklyanin Algebra; Degenerate Sklyanin Algebra; Deformed Sklyanin Algebra; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Walton, C. M. (2011). On Degenerations and Deformations of Sklyanin Algebras. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/86397

Chicago Manual of Style (16^th Edition):

Walton, Chelsea M. “On Degenerations and Deformations of Sklyanin Algebras.” 2011. Doctoral Dissertation, University of Michigan. Accessed January 24, 2021. http://hdl.handle.net/2027.42/86397.

MLA Handbook (7^th Edition):

Walton, Chelsea M. “On Degenerations and Deformations of Sklyanin Algebras.” 2011. Web. 24 Jan 2021.

Vancouver:

Walton CM. On Degenerations and Deformations of Sklyanin Algebras. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/2027.42/86397.

Council of Science Editors:

Walton CM. On Degenerations and Deformations of Sklyanin Algebras. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/86397

Tartu University

8. Bazunova, Nadezda. Differential calculus d3 = 0 on binary and ternary associative algebras .

Degree: 2011, Tartu University

URL: http://hdl.handle.net/10062/18102

► Antud väitekiri on pühendatud mittekommutatiivse geomeetria raames tekkinud diferent-siaalarvutusele diferentsiaaliga d, mis rahuldab tingimust d³=0. Antud diferentsiaalarvutus tugineb gradueeritud Q-diferentsiaalalgebra mõistele, kus Q on kuupjuur… (more)

▼ Antud väitekiri on pühendatud mittekommutatiivse geomeetria raames tekkinud diferent-siaalarvutusele diferentsiaaliga d, mis rahuldab tingimust d³=0. Antud diferentsiaalarvutus tugineb gradueeritud Q-diferentsiaalalgebra mõistele, kus Q on kuupjuur ühest. Gradueeritud Q-diferentsiaalalgebrat võib vaadelda gradueeritud diferentsiaalalgebra üldistusena, kusjuures gradueeritud diferentsiaalalgebrad mängivad tähtsat rolli nii kaasaegses diferentsiaalgeomeet- rias kui ka väljateooriates. Esimeses peatükis antakse esimest järku diferentsiaalarvutuse assotsiatiivsetel algebratel de-tailne kirjeldus, seejärel vaadeldakse koordinaatdiferentsiaalarvutust, mis tekib juhul, kui al-gebra A on lõplikult tekitatud algebra ja A-bimoodul M kui parempoolne A-moodul on vaba. Näidatakse, et koordinaatdiferentsiaalarvutuse korral diferentsiaal d tekitab parempoolsed osatuletised algebral A, mis rahuldavad teatud homomorfismiga deformeeritud Leibnizi vale-mit. Antakse universaalse esimest järku diferentsiaalarvutuse ja gradueeritud diferentsiaal-algebra struktuuri detailne kirjeldus. Teises peatükis uuritakse gradueeritud diferentsiaalalgebra üldistust, mis tekkis mittekommu-tatiivse geomeetria raames 1990-ndatel aastatel. Seda üldistust nimetatakse gradueeritud q-di-ferentsiaalalgebraks ja teises peatükis antakse selle üldistuse definitsioon. Gradueeritud q-di-ferentsiaalalgebra diferentsiaal d rahuldab tingimust d^N=0, kus N≠2. Teises peatükis on vaa-deldud esimest mittetriviaalset üldistust, kus q on kuupjuur ühest ja diferentsiaal rahuldab d³=0. Gradueeritud Q-diferentsiaalalgebra rakendustes mittekommutatiivses geomeetrias ja teoreetilises füüsikas on tähtis probleem, kuidas konstrueerida gradueeritud q-diferentsiaal-algebra, kui on antud esimest järku diferentsiaalarvutus assotsiatiivsel algebral. Teises peatü-kis näidatakse, kuidas konstrueerida gradueeritud Q-diferentsiaalalgebrat, kui on antud esi-mest järku diferentsiaalarvutus algebral, mis on lõplikult tekitatud teatuid seoseid rahuldavate moodustajate poolt. Kolmandas peatükis rakendatakse teises peatükis välja töötatud meetodit diferentsiaalvormi-de algebra analoogi konstrueerimiseks järgmistel ruumidel: anioonilisel (anyonic) ühedimen-sionaalsel ruumil, ruutalgebral, h-deformeeritud kvanttasandil, q-deformeeritud kvanttasandil. On antud diferentsiaalvormide algebra analoogi detailne kirjeldus, kusjuures on leitud kõik kommutatsiooniseosed koordinaatide ja nende diferentsiaalide vahel. Ühedimensionaalse ruu-mi korral on näidatud, et diferentsiaalvormide algebra struktuuri erinevad komponendid on kooskõlas, kui ühedimensionaalne ruum on aniooniline. On näidatud, et anioonilise ruumi korral diferentsiaalvormide algebra analoog sisaldab esimest järku diferentsiaalarvutust, mida kasutatakse murdsupersümmeetrilistes teooriates. Viimases peatükis vaadeldakse diferentsiaalarvutust d³=0 ternaarsetel algebratel. On antud ternaarse algebra struktuuri ja sellega seotud mõistete (ternaarne assotsiatiivsus, involutsioon, struktuurikonstandid) lühikirjeldus. On…

Subjects/Keywords: mittekommutatiivne algebra; diferentsisaalgeomeetria; diferentsiaalarvutus; noncommutative algebra; differential geometry; differential calculus

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APA (6^th Edition):

Bazunova, N. (2011). Differential calculus d3 = 0 on binary and ternary associative algebras . (Thesis). Tartu University. Retrieved from http://hdl.handle.net/10062/18102

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bazunova, Nadezda. “Differential calculus d3 = 0 on binary and ternary associative algebras .” 2011. Thesis, Tartu University. Accessed January 24, 2021. http://hdl.handle.net/10062/18102.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bazunova, Nadezda. “Differential calculus d3 = 0 on binary and ternary associative algebras .” 2011. Web. 24 Jan 2021.

Vancouver:

Bazunova N. Differential calculus d3 = 0 on binary and ternary associative algebras . [Internet] [Thesis]. Tartu University; 2011. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/10062/18102.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bazunova N. Differential calculus d3 = 0 on binary and ternary associative algebras . [Thesis]. Tartu University; 2011. Available from: http://hdl.handle.net/10062/18102

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

9. Heinle, Albert. Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations.

Degree: 2016, University of Waterloo

URL: http://hdl.handle.net/10012/10948

► Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In… (more)

▼ Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In the Ph.D. studies leading to this thesis, the focus was mainly on two areas: Factorization in certain noncommutative domains and matrix normal forms over noncommutative principal ideal domains. Regarding the area of factorization, we initialize in this thesis a classification of noncommutative domains with respect to the factorization properties of their elements. Such a classification is well established in the area of commutative integral domains. Specifically, we define conditions to identify so-called finite factorization domains, and discover that the ubiquitous G-algebras are finite factorization domains. We furthermore realize a practical factorization algorithm applicable to G-algebras, with minor assumptions on the underlying field. Since the generality of our algorithm comes with the price of performance, we also study how it can be optimized for specific domains. Moreover, all of these factorization algorithms are implemented. However, it turns out that factorization is difficult for many types of noncommutative rings. This observation leads to the adjunct examination of noncommutative rings in the context of cryptography. In particular, we develop a Diffie-Hellman-like key exchange protocol based on certain noncommutative rings. Regarding the matrix normal forms, we present a polynomial-time algorithm of Las Vegas type to compute the Jacobson normal form of matrices over specific domains. We will study the flexibility, as well as the limitations of our proposal. Another core contribution of this thesis consists of various implementations to assist future researchers working with noncommutative algebras. Detailed reports on all these programs and software-libraries are provided. We furthermore develop a benchmarking tool called SDEval, tailored to the needs of the computer algebra community. A description of this tool is also included in this thesis.

Subjects/Keywords: Noncommutative Algebra; Symbolic Computation; Computer Algebra; Matrix Normal Forms; Cryptography

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APA (6^th Edition):

Heinle, A. (2016). Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/10948

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Heinle, Albert. “Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations.” 2016. Thesis, University of Waterloo. Accessed January 24, 2021. http://hdl.handle.net/10012/10948.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Heinle, Albert. “Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations.” 2016. Web. 24 Jan 2021.

Vancouver:

Heinle A. Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations. [Internet] [Thesis]. University of Waterloo; 2016. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/10012/10948.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Heinle A. Computational Approaches to Problems in Noncommutative Algebra – Theory, Applications and Implementations. [Thesis]. University of Waterloo; 2016. Available from: http://hdl.handle.net/10012/10948

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

The Ohio State University

10. Schoenecker, Kevin J. An infinite family of anticommutative algebras with a cubic form.

Degree: PhD, Mathematics, 2007, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

► A noncommutative Jordan Algebra, J, of degree two can be constructed from an anticommutative algebra S that has a symmetric associative bilinear form. If additional… (more)

Subjects/Keywords: Mathematics; anticommutative algebra; noncommutative Jordan algebra

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APA (6^th Edition):

Schoenecker, K. J. (2007). An infinite family of anticommutative algebras with a cubic form. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

Chicago Manual of Style (16^th Edition):

Schoenecker, Kevin J. “An infinite family of anticommutative algebras with a cubic form.” 2007. Doctoral Dissertation, The Ohio State University. Accessed January 24, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559.

MLA Handbook (7^th Edition):

Schoenecker, Kevin J. “An infinite family of anticommutative algebras with a cubic form.” 2007. Web. 24 Jan 2021.

Vancouver:

Schoenecker KJ. An infinite family of anticommutative algebras with a cubic form. [Internet] [Doctoral dissertation]. The Ohio State University; 2007. [cited 2021 Jan 24]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559.

Council of Science Editors:

Schoenecker KJ. An infinite family of anticommutative algebras with a cubic form. [Doctoral Dissertation]. The Ohio State University; 2007. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1187185559

University of California – San Diego

11. Elle, Susan. A study of dimension 5 Ore extensions.

Degree: Mathematics, 2016, University of California – San Diego

URL: http://www.escholarship.org/uc/item/51s8q9xd

► In order to study AS-regular algebras of dimension 5, we consider dimension 5 graded iterated Ore extensions generated in degree one. We present an interesting… (more)

Subjects/Keywords: Mathematics; Algebra; Artin-Schelter regular; Noncommutative; Ore; Ring

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APA (6^th Edition):

Elle, S. (2016). A study of dimension 5 Ore extensions. (Thesis). University of California – San Diego. Retrieved from http://www.escholarship.org/uc/item/51s8q9xd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Elle, Susan. “A study of dimension 5 Ore extensions.” 2016. Thesis, University of California – San Diego. Accessed January 24, 2021. http://www.escholarship.org/uc/item/51s8q9xd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Elle, Susan. “A study of dimension 5 Ore extensions.” 2016. Web. 24 Jan 2021.

Vancouver:

Elle S. A study of dimension 5 Ore extensions. [Internet] [Thesis]. University of California – San Diego; 2016. [cited 2021 Jan 24]. Available from: http://www.escholarship.org/uc/item/51s8q9xd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Elle S. A study of dimension 5 Ore extensions. [Thesis]. University of California – San Diego; 2016. Available from: http://www.escholarship.org/uc/item/51s8q9xd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

12. Peterka, Mira Alexander. Finitely-Generated Projective Modules over $theta$-deformed Spheres.

Degree: Mathematics, 2010, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/4cx22565

► We investigate the ``θ-deformed spheres" C(S³_θ) and C(S⁴_θ) for the case θ an irrational number. We show that all finitely-generated projective modules over C(S³_θ) are… (more)

Subjects/Keywords: Mathematics; Gauge Theory; K-theory; Noncommutative Geometry; Quantum Algebra

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APA (6^th Edition):

Peterka, M. A. (2010). Finitely-Generated Projective Modules over $theta$-deformed Spheres. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/4cx22565

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Peterka, Mira Alexander. “Finitely-Generated Projective Modules over $theta$-deformed Spheres.” 2010. Thesis, University of California – Berkeley. Accessed January 24, 2021. http://www.escholarship.org/uc/item/4cx22565.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Peterka, Mira Alexander. “Finitely-Generated Projective Modules over $theta$-deformed Spheres.” 2010. Web. 24 Jan 2021.

Vancouver:

Peterka MA. Finitely-Generated Projective Modules over $theta$-deformed Spheres. [Internet] [Thesis]. University of California – Berkeley; 2010. [cited 2021 Jan 24]. Available from: http://www.escholarship.org/uc/item/4cx22565.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Peterka MA. Finitely-Generated Projective Modules over $theta$-deformed Spheres. [Thesis]. University of California – Berkeley; 2010. Available from: http://www.escholarship.org/uc/item/4cx22565

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Drexel University

13. Abduvalieva, Gulnara K. Fixed-point and implicit/inverse function theorems for free noncommutative functions.

Degree: 2015, Drexel University

URL: http://hdl.handle.net/1860/idea:6318

►

We establish a fixed-point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions… (more)

Subjects/Keywords: Mathematics; Noncommutative algebras; Banach modules (Algebra); Mappings (Mathematics)

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APA (6^th Edition):

Abduvalieva, G. K. (2015). Fixed-point and implicit/inverse function theorems for free noncommutative functions. (Thesis). Drexel University. Retrieved from http://hdl.handle.net/1860/idea:6318

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Abduvalieva, Gulnara K. “Fixed-point and implicit/inverse function theorems for free noncommutative functions.” 2015. Thesis, Drexel University. Accessed January 24, 2021. http://hdl.handle.net/1860/idea:6318.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Abduvalieva, Gulnara K. “Fixed-point and implicit/inverse function theorems for free noncommutative functions.” 2015. Web. 24 Jan 2021.

Vancouver:

Abduvalieva GK. Fixed-point and implicit/inverse function theorems for free noncommutative functions. [Internet] [Thesis]. Drexel University; 2015. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1860/idea:6318.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Abduvalieva GK. Fixed-point and implicit/inverse function theorems for free noncommutative functions. [Thesis]. Drexel University; 2015. Available from: http://hdl.handle.net/1860/idea:6318

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

14. Davies, Andrew Phillip. Cocycle Twists of Algebras.

Degree: 2014, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:229719

See main text. Advisors/Committee Members: PREMET, ALEXANDER AA, Premet, Alexander, Stafford, Toby.

Subjects/Keywords: noncommutative algebra; cocycle twist

…truncated point module, 36 N-graded algebra, 24 N-graded module, 25 noncommutative Pn−1 , 32 k… …graded algebra, 24 AS-Gorenstein, 69 G-grading, 15 AS-regular, 69 generalised THCR, see… …algebra, 164 Cohen-Macaulay, (CM), 78 group algebra, 46 connected graded, (c.g… …11 INDEX OF TERMINOLOGY 12 line module, 41 Sklyanin algebra, 4-dimensional, 19, 88… …Noncommutative Serre’s theorem, 31 noncommutative space, 29 normalising sequence, 164 twisted group…

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APA (6^th Edition):

Davies, A. P. (2014). Cocycle Twists of Algebras. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:229719

Chicago Manual of Style (16^th Edition):

Davies, Andrew Phillip. “Cocycle Twists of Algebras.” 2014. Doctoral Dissertation, University of Manchester. Accessed January 24, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:229719.

MLA Handbook (7^th Edition):

Davies, Andrew Phillip. “Cocycle Twists of Algebras.” 2014. Web. 24 Jan 2021.

Vancouver:

Davies AP. Cocycle Twists of Algebras. [Internet] [Doctoral dissertation]. University of Manchester; 2014. [cited 2021 Jan 24]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:229719.

Council of Science Editors:

Davies AP. Cocycle Twists of Algebras. [Doctoral Dissertation]. University of Manchester; 2014. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:229719

University of Iowa

15. Norton, Rachael M. Pick interpolation, displacement equations, and W*-correspondences.

Degree: PhD, Mathematics, 2017, University of Iowa

URL: https://ir.uiowa.edu/etd/5586

► The classical Nevanlinna-Pick interpolation theorem, proved in 1915 by Pick and in 1919 by Nevanlinna, gives a condition for when there exists an interpolating… (more)

▼ The classical Nevanlinna-Pick interpolation theorem, proved in 1915 by Pick and in 1919 by Nevanlinna, gives a condition for when there exists an interpolating function in H∞(D) for a specified set of data in the complex plane. In 1967, Sarason proved his commutant lifting theorem for H∞(D), from which an operator theoretic proof of the classical Nevanlinna-Pick theorem followed. Several competing noncommutative generalizations arose as a consequence of Sarason's result, and two strategies emerged for proving generalized Nevanlinna-Pick theorems: via a commutant lifting theorem or via a resolvent, or displacement, equation. We explore the difference between these two approaches. Specifically, we compare two theorems: one by Constantinescu-Johnson from 2003 and one by Muhly-Solel from 2004. Muhly-Solel's theorem is stated in the highly general context of W*-correspondences and is proved via commutant lifting. Constantinescu-Johnson's theorem, while stated in a less general context, has the advantage of an elegant proof via a displacement equation. In order to make the comparison, we first generalize Constantinescu-Johnson's theorem to the setting of W*-correspondences in Theorem 3.0.1. Our proof, modeled after Constantinescu-Johnson's, hinges on a modified version of their displacement equation. Then we show that Theorem 3.0.1 is fundamentally different from Muhly-Solel's. More specifically, interpolation in the sense of Muhly-Solel's theorem implies interpolation in the sense of Theorem 3.0.1, but the converse is not true. Nevertheless, we identify a commutativity assumption under which the two theorems yield the same result. In addition to the two main theorems, we include smaller results that clarify the connections between the notation, space of interpolating maps, and point evaluation employed by Constantinescu-Johnson and those employed by Muhly-Solel. We conclude with an investigation of the relationship between Theorem 3.0.1 and Popescu's generalized Nevanlinna-Pick theorem proved in 2003. Advisors/Committee Members: Muhly, Paul S. (supervisor).

Subjects/Keywords: displacement equation; Nevanlinna-Pick interpolation; noncommutative Hardy algebra; W*-correspondence; Mathematics

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APA (6^th Edition):

Norton, R. M. (2017). Pick interpolation, displacement equations, and W*-correspondences. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/5586

Chicago Manual of Style (16^th Edition):

Norton, Rachael M. “Pick interpolation, displacement equations, and W*-correspondences.” 2017. Doctoral Dissertation, University of Iowa. Accessed January 24, 2021. https://ir.uiowa.edu/etd/5586.

MLA Handbook (7^th Edition):

Norton, Rachael M. “Pick interpolation, displacement equations, and W*-correspondences.” 2017. Web. 24 Jan 2021.

Vancouver:

Norton RM. Pick interpolation, displacement equations, and W*-correspondences. [Internet] [Doctoral dissertation]. University of Iowa; 2017. [cited 2021 Jan 24]. Available from: https://ir.uiowa.edu/etd/5586.

Council of Science Editors:

Norton RM. Pick interpolation, displacement equations, and W*-correspondences. [Doctoral Dissertation]. University of Iowa; 2017. Available from: https://ir.uiowa.edu/etd/5586

University of Houston

16. Wang, Zhenhua 1988-. Theory of Jordan Operator Algebras and Operator *-Algebras.

Degree: PhD, Mathematics, 2019, University of Houston

URL: http://hdl.handle.net/10657/4656

► An operator algebra is a closed subalgebra of B(H), for a complex Hilbert space H. By a Jordan operator algebra, we mean a norm-closed Jordan… (more)

Subjects/Keywords: Jordan algebras; Algebra; Operator algebras; Noncommutative topology; Open projection

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APA (6^th Edition):

Wang, Z. 1. (2019). Theory of Jordan Operator Algebras and Operator *-Algebras. (Doctoral Dissertation). University of Houston. Retrieved from http://hdl.handle.net/10657/4656

Chicago Manual of Style (16^th Edition):

Wang, Zhenhua 1988-. “Theory of Jordan Operator Algebras and Operator *-Algebras.” 2019. Doctoral Dissertation, University of Houston. Accessed January 24, 2021. http://hdl.handle.net/10657/4656.

MLA Handbook (7^th Edition):

Wang, Zhenhua 1988-. “Theory of Jordan Operator Algebras and Operator *-Algebras.” 2019. Web. 24 Jan 2021.

Vancouver:

Wang Z1. Theory of Jordan Operator Algebras and Operator *-Algebras. [Internet] [Doctoral dissertation]. University of Houston; 2019. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/10657/4656.

Council of Science Editors:

Wang Z1. Theory of Jordan Operator Algebras and Operator *-Algebras. [Doctoral Dissertation]. University of Houston; 2019. Available from: http://hdl.handle.net/10657/4656

University of Edinburgh

17. Russell, Ewan. Prime ideals in quantum algebras.

Degree: PhD, 2009, University of Edinburgh

URL: http://hdl.handle.net/1842/3450

► The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo… (more)

▼ The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are noncommutative analogues of coordinate rings of algebraic varieties. The organic nature by which these algebras arose is of great interest to algebraists. In particular, investigating ring theoretic properties of these noncommutative algebras in comparison to the properties already known about their classical (commutative) counterparts proves to be a fruitful process. The prime spectrum of an algebra has always been seen as an important key to understanding its fundamental structure. The search for prime spectra is a central focus of this thesis. Our focus is mainly on Quantum Grassmannian subalgebras of quantized coordinate rings of Matrices of size m x n (denoted Oq(Mm;n)). Quantum Grassmannians of size m x n are denoted Gq(m; n) and are the subalgebras generated by the maximal quantum minors of Oq(Mm;n). In Chapter 2 we look at the simplest interesting case, namely the 2 x 4 Quantum Grassmannian (Gq(2; 4)), and we identify the H-primes and automorphism group of this algebra. Chapter 3 begins with a very important result concerning the dehomogenisation isomorphism linking Gq(m; n) and Oq(Mm;n¡m). This result is applied to help to identify H-prime spectra of Quantum Grassmannians. Chapter 4 focuses on identifying the number of H-prime ideals in the 2xn Quan- tum Grassmannian. We show the link between Cauchon fillings of subpartitions and H-prime ideals. In Chapter 5, we look at methods of ordering the generating elements of Quantum Grassmannians and prove the result that Quantum Grassmannians are Quantum Graded Algebras with a Straightening Law is maintained on using one of these alternative orderings. Chapter 6 looks at the Poisson structure on the commutative coordinate ring, G(2; 4) encoded by the noncommutative quantized algebra Gq(2; 4). We describe the symplectic ideals of G(2; 4) based on this structure. Finally in Chapter 7, we present an analysis of the 2 x 2 Reflection Equation Algebra and its primes. This algebra is obtained from the quantized coordinate ring of 2 x 2 matrices, Oq(M2;2).

Subjects/Keywords: 510; algebra; noncommutative algebras

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APA (6^th Edition):

Russell, E. (2009). Prime ideals in quantum algebras. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/3450

Chicago Manual of Style (16^th Edition):

Russell, Ewan. “Prime ideals in quantum algebras.” 2009. Doctoral Dissertation, University of Edinburgh. Accessed January 24, 2021. http://hdl.handle.net/1842/3450.

MLA Handbook (7^th Edition):

Russell, Ewan. “Prime ideals in quantum algebras.” 2009. Web. 24 Jan 2021.

Vancouver:

Russell E. Prime ideals in quantum algebras. [Internet] [Doctoral dissertation]. University of Edinburgh; 2009. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1842/3450.

Council of Science Editors:

Russell E. Prime ideals in quantum algebras. [Doctoral Dissertation]. University of Edinburgh; 2009. Available from: http://hdl.handle.net/1842/3450

University of Washington

18. McMurdie, Christopher Robert. The C*-algebra of a finite T_0 topological space.

Degree: PhD, 2015, University of Washington

URL: http://hdl.handle.net/1773/34025

► We are concerned with the following motivating question: how can one extend the classical Gelfand-Naimark theorem to the simplest non-Hausdorff topological spaces? Our model space… (more)

Subjects/Keywords: algebra; bimodule; geometry; Hilbert; noncommutative; poset; Mathematics; mathematics

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APA (6^th Edition):

McMurdie, C. R. (2015). The C*-algebra of a finite T_0 topological space. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/34025

Chicago Manual of Style (16^th Edition):

McMurdie, Christopher Robert. “The C*-algebra of a finite T_0 topological space.” 2015. Doctoral Dissertation, University of Washington. Accessed January 24, 2021. http://hdl.handle.net/1773/34025.

MLA Handbook (7^th Edition):

McMurdie, Christopher Robert. “The C*-algebra of a finite T_0 topological space.” 2015. Web. 24 Jan 2021.

Vancouver:

McMurdie CR. The C*-algebra of a finite T_0 topological space. [Internet] [Doctoral dissertation]. University of Washington; 2015. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1773/34025.

Council of Science Editors:

McMurdie CR. The C*-algebra of a finite T_0 topological space. [Doctoral Dissertation]. University of Washington; 2015. Available from: http://hdl.handle.net/1773/34025

University of Edinburgh

19. Crawford, Simon Philip. Singularities of noncommutative surfaces.

Degree: PhD, 2018, University of Edinburgh

URL: http://hdl.handle.net/1842/31543

► The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also… (more)

▼ The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite global dimension. Very little is known about singularities of noncommutative rings, particularly those which are not finite over their centre. In this thesis, we are able to give a precise description of the singularities of a few families of examples. In many examples, we lay the foundations of noncommutative singularity theory by giving a precise description of the singularities of the fundamental examples of noncommutative surfaces. We draw comparisons with the fundamental examples of commutative surface singularities, called Kleinian singularities, which arise from the action of a finite subgroup of SL(2; k) acting on a polynomial ring. The main tool we use to study the singularities of noncommutative surfaces is the singularity category, first introduced by Buchweitz in [Buc86]. This takes a (possibly noncommutative) ring R and produces a triangulated category Dsg(R) which provides a measure of "how singular" R is. Roughly speaking, the size of this category reflects how bad the singularity is; in particular, Dsg(R) is trivial if and only if R has finite global dimension. In [CBH98], Crawley-Boevey-Holland introduced a family of noncommutative rings which can be thought of as deformations of the coordinate ring of a Kleinian singularity. We give a precise description of the singularity categories of these deformations, and show that their singularities can be thought of as unions of (commutative) Kleinian singularities. In particular, our results show that deforming a singularity in this setting makes it no worse. Another family of noncommutative surfaces were introduced by Rogalski-Sierra-Stafford in [RSS15b]. The authors showed that these rings share a number of ring-theoretic properties with deformations of type A Kleinian singularities. We apply our techniques to show that the "least singular" example has an A1 singularity, and conjecture that other examples exhibit similar behaviour. In [CKWZ16a], Chan-Kirkman-Walton-Zhang gave a definition for a quantum version of Kleinian singularities. These require the data of a two-dimensional AS regular algebra A and a finite group G acting on A with trivial homological determinant. We extend a number of results in [CBH98] to the setting of quantum Kleinian singularities. More precisely, we show that one can construct deformations of the skew group rings A#G and the invariant rings AG, and then determine some of their ring-theoretic properties. These results allow us to give a precise description of the singularity categories of quantum Kleinian singularities, which often have very different behaviour to their non-quantum analogues.

Subjects/Keywords: 512; ring theory; abstract algebra; commutative ring; singular points; noncommutative surfaces

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APA (6^th Edition):

Crawford, S. P. (2018). Singularities of noncommutative surfaces. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/31543

Chicago Manual of Style (16^th Edition):

Crawford, Simon Philip. “Singularities of noncommutative surfaces.” 2018. Doctoral Dissertation, University of Edinburgh. Accessed January 24, 2021. http://hdl.handle.net/1842/31543.

MLA Handbook (7^th Edition):

Crawford, Simon Philip. “Singularities of noncommutative surfaces.” 2018. Web. 24 Jan 2021.

Vancouver:

Crawford SP. Singularities of noncommutative surfaces. [Internet] [Doctoral dissertation]. University of Edinburgh; 2018. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1842/31543.

Council of Science Editors:

Crawford SP. Singularities of noncommutative surfaces. [Doctoral Dissertation]. University of Edinburgh; 2018. Available from: http://hdl.handle.net/1842/31543

Kent State University

20. Catalano, Louisa. On maps preserving products.

Degree: PhD, College of Arts and Sciences / Department of Mathematical Science, 2020, Kent State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=kent1594320429310821

► Maps characterized by their action on some equal products have often been studied in Functional Analysis and Linear Algebra. We will describe maps that act… (more)

Subjects/Keywords: Mathematics; noncommutative algebra, functional identities, linear preserver problems

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APA (6^th Edition):

Catalano, L. (2020). On maps preserving products. (Doctoral Dissertation). Kent State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=kent1594320429310821

Chicago Manual of Style (16^th Edition):

Catalano, Louisa. “On maps preserving products.” 2020. Doctoral Dissertation, Kent State University. Accessed January 24, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1594320429310821.

MLA Handbook (7^th Edition):

Catalano, Louisa. “On maps preserving products.” 2020. Web. 24 Jan 2021.

Vancouver:

Catalano L. On maps preserving products. [Internet] [Doctoral dissertation]. Kent State University; 2020. [cited 2021 Jan 24]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1594320429310821.

Council of Science Editors:

Catalano L. On maps preserving products. [Doctoral Dissertation]. Kent State University; 2020. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1594320429310821

21. Davies, Andrew Phillip. Cocycle twists of algebras.

Degree: PhD, 2014, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/cocycle-twists-of-algebras(23710bc8-abdf-4b8d-9836-111164fefc11).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618077

Subjects/Keywords: 512; Noncommutative algebra, Cocycle twist

…truncated point module, 36 N-graded algebra, 24 N-graded module, 25 noncommutative Pn−1 , 32 k… …noncommutative space to a c.g. algebra, one can ask the following two questions to motivate the… …graded algebra, 24 AS-Gorenstein, 69 G-grading, 15 AS-regular, 69 generalised THCR, see… …algebra, 164 Cohen-Macaulay, (CM), 78 group algebra, 46 connected graded, (c.g… …11 INDEX OF TERMINOLOGY 12 line module, 41 Sklyanin algebra, 4-dimensional, 19, 88…

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APA (6^th Edition):

Davies, A. P. (2014). Cocycle twists of algebras. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/cocycle-twists-of-algebras(23710bc8-abdf-4b8d-9836-111164fefc11).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618077

Chicago Manual of Style (16^th Edition):

Davies, Andrew Phillip. “Cocycle twists of algebras.” 2014. Doctoral Dissertation, University of Manchester. Accessed January 24, 2021. https://www.research.manchester.ac.uk/portal/en/theses/cocycle-twists-of-algebras(23710bc8-abdf-4b8d-9836-111164fefc11).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618077.

MLA Handbook (7^th Edition):

Davies, Andrew Phillip. “Cocycle twists of algebras.” 2014. Web. 24 Jan 2021.

Vancouver:

Davies AP. Cocycle twists of algebras. [Internet] [Doctoral dissertation]. University of Manchester; 2014. [cited 2021 Jan 24]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/cocycle-twists-of-algebras(23710bc8-abdf-4b8d-9836-111164fefc11).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618077.

Council of Science Editors:

Davies AP. Cocycle twists of algebras. [Doctoral Dissertation]. University of Manchester; 2014. Available from: https://www.research.manchester.ac.uk/portal/en/theses/cocycle-twists-of-algebras(23710bc8-abdf-4b8d-9836-111164fefc11).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618077

University of Washington

22. Casper, William Riley. Bispectral Operator Algebras.

Degree: PhD, 2017, University of Washington

URL: http://hdl.handle.net/1773/40239

► This dissertation is an amalgamation of various results on the structure of bispectral differential operator algebras, ie. algebras of differential operators with possibly noncommutative coefficients… (more)

Subjects/Keywords: Bispectral problem; Differential operators; Noncommutative algebra; Operator algebras; Orthogonal Polynomials; Mathematics; Mathematics

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APA (6^th Edition):

Casper, W. R. (2017). Bispectral Operator Algebras. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/40239

Chicago Manual of Style (16^th Edition):

Casper, William Riley. “Bispectral Operator Algebras.” 2017. Doctoral Dissertation, University of Washington. Accessed January 24, 2021. http://hdl.handle.net/1773/40239.

MLA Handbook (7^th Edition):

Casper, William Riley. “Bispectral Operator Algebras.” 2017. Web. 24 Jan 2021.

Vancouver:

Casper WR. Bispectral Operator Algebras. [Internet] [Doctoral dissertation]. University of Washington; 2017. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1773/40239.

Council of Science Editors:

Casper WR. Bispectral Operator Algebras. [Doctoral Dissertation]. University of Washington; 2017. Available from: http://hdl.handle.net/1773/40239

Utah State University

23. Bowles, Tyler B. Universal Localizations of Certain Noncommutative Rings.

Degree: MS, Mathematics and Statistics, 2020, Utah State University

URL: https://digitalcommons.usu.edu/etd/7881

► A common theme throughout algebra is the extension of arithmetic systems to ones over which new equations can be solved. For instance, someone who… (more)

▼ A common theme throughout algebra is the extension of arithmetic systems to ones over which new equations can be solved. For instance, someone who knows only positive numbers might think that there is no solution to x + 3 = 0, yet later learns x = ‚àí3 to be a feasible solution. Likewise, when faced with the equation 2x = 3, someone familiar only with integers may declare that there is no solution, but may later learn that x = 3/2 is a reasonable answer. Many eventually learn that the extension of real numbers to complex numbers unlocks solutions to previously unsolvable equations, such as x² = ‚àí1. In algebra, a ring is, roughly speaking, any arithmetic system in which addition and multiplication behave ‚Äúreasonably‚Äù, while a homomorphism is a function that is compatible with the appropriate arithmetic systems. Some rings are noncommutative, meaning that the order in which one multiplies may change the product (i.e.ab ‚â† ba), in contrast to most grade school arithmetic. The extension of integers to rational numbers that allows one to solve 2x = 3 is an example of a more general technique, called localization. For commutative rings, localization is well understood and allows one to reasonably form fraction-like objects with numerators and denominators so that one can solve any equation of the form ax = b. However, this process becomes much more difficult for noncommutative rings. A modern perspective on this problem asks more broadly for an extension of a noncommutative ring which makes any given homomorphism invertible, making it possible to solve certain equations involving the homomorphism. In general, satisfactory descriptions for extensions of this type are elusive. However, there are circumstances in which it is possible to give a concrete answer. We investigate a class of rings called the generalized triangular matrix rings whose elements are matrix-like. Our study focuses on homomorphisms whose inputs and outputs are each columns from these matrices. The results explicitly describe all of the extensions that result in available inverse homomorphisms. These extensions, called universal localizations of the ring, are also rings whose elements are matrix-like, and these matrices are more symmetric than the ring before localization. To provide some historical context, we also recount the developments in the theory that led to this research. This includes detailed descriptions of classical localization and its counterpart in noncommutative algebra, Ore localization, as well as accounts of modern viewpoints, namely Cohn localization and universal adjunction. Advisors/Committee Members: Dariusz M. Wilczy≈Ñski, Nathan Geer, Zhaohu Nie, ;.

Subjects/Keywords: universal localization; Cohn localization; Ore localization; localization; rings; modules; fields; fractions; matrix rings; noncommutative; algebra; Algebra; Mathematics

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APA (6^th Edition):

Bowles, T. B. (2020). Universal Localizations of Certain Noncommutative Rings. (Masters Thesis). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7881

Chicago Manual of Style (16^th Edition):

Bowles, Tyler B. “Universal Localizations of Certain Noncommutative Rings.” 2020. Masters Thesis, Utah State University. Accessed January 24, 2021. https://digitalcommons.usu.edu/etd/7881.

MLA Handbook (7^th Edition):

Bowles, Tyler B. “Universal Localizations of Certain Noncommutative Rings.” 2020. Web. 24 Jan 2021.

Vancouver:

Bowles TB. Universal Localizations of Certain Noncommutative Rings. [Internet] [Masters thesis]. Utah State University; 2020. [cited 2021 Jan 24]. Available from: https://digitalcommons.usu.edu/etd/7881.

Council of Science Editors:

Bowles TB. Universal Localizations of Certain Noncommutative Rings. [Masters Thesis]. Utah State University; 2020. Available from: https://digitalcommons.usu.edu/etd/7881

University of Victoria

24. Duwenig, Anna. Poincaré self-duality of A_θ.

Degree: Department of Mathematics and Statistics, 2020, University of Victoria

URL: http://hdl.handle.net/1828/11678

► The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was… (more)

Subjects/Keywords: irrational rotation algebra; KK-theory; abstract transversal; groupoid; Kronecker Flow; noncommutative torus; Poincaré duality; Kasparov product; unbounded operator; noncommutative geometry; bivariant K-theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Duwenig, A. (2020). Poincaré self-duality of A_θ. (Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/11678

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Duwenig, Anna. “Poincaré self-duality of A_θ.” 2020. Thesis, University of Victoria. Accessed January 24, 2021. http://hdl.handle.net/1828/11678.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Duwenig, Anna. “Poincaré self-duality of A_θ.” 2020. Web. 24 Jan 2021.

Vancouver:

Duwenig A. Poincaré self-duality of A_θ. [Internet] [Thesis]. University of Victoria; 2020. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1828/11678.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Duwenig A. Poincaré self-duality of A_θ. [Thesis]. University of Victoria; 2020. Available from: http://hdl.handle.net/1828/11678

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

25. Mello, Thiago Castilho de, 1984-. Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra.

Degree: 2012, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366

► Abstract: In this thesis, we study the generic algebra of M1;1 in two generators over an infinite field of characteristic different from 2. We describe… (more)

Subjects/Keywords: Identidade polinomial; Grassmann, Álgebra de; Anéis (Álgebra); PI-álgebras; Álgebra não-comutativa; Polynomial identity; Grassmann algebra; Rings (Algebra); PI-algebra; Noncommutative algebras

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APA (6^th Edition):

Mello, Thiago Castilho de, 1. (2012). Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mello, Thiago Castilho de, 1984-. “Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra.” 2012. Thesis, Universidade Estadual de Campinas. Accessed January 24, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mello, Thiago Castilho de, 1984-. “Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra.” 2012. Web. 24 Jan 2021.

Vancouver:

Mello, Thiago Castilho de 1. Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Jan 24]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mello, Thiago Castilho de 1. Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann: Polynomial identities in matrix algebras over the Grassmann algebra. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université de Montréal

26. Kratsios, Anastasis. Bounding The Hochschild Cohomological Dimension.

Degree: 2015, Université de Montréal

URL: http://hdl.handle.net/1866/12814

Subjects/Keywords: Relative Homological Algebra; Dimension Theory; Noncommutative Geometry; Hochschild Cohomology; Noncommutative Algebra; Algebraic Geometry; Homological Algebra; Algèbre homologique; Géométrie Algébrique; Noncommutative Differential Forms; Mathematics / Mathématiques (UMI : 0405)

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APA (6^th Edition):

Kratsios, A. (2015). Bounding The Hochschild Cohomological Dimension. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/12814

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kratsios, Anastasis. “Bounding The Hochschild Cohomological Dimension.” 2015. Thesis, Université de Montréal. Accessed January 24, 2021. http://hdl.handle.net/1866/12814.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kratsios, Anastasis. “Bounding The Hochschild Cohomological Dimension.” 2015. Web. 24 Jan 2021.

Vancouver:

Kratsios A. Bounding The Hochschild Cohomological Dimension. [Internet] [Thesis]. Université de Montréal; 2015. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1866/12814.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kratsios A. Bounding The Hochschild Cohomological Dimension. [Thesis]. Université de Montréal; 2015. Available from: http://hdl.handle.net/1866/12814

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Galvão, Lucas. A dimensão de Gelfand-Kirillov de certas álgebras.

Degree: Mestrado, Matemática, 2014, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/ ;

►

A dimensão de Gelfand-Kirillov mede a taxa de crescimento assintótico de álgebras. Como fornece informações importantes sobre a sua estrutura, este invariante se tornou uma… (more)

Subjects/Keywords: Álgebra não-comutativa; Crescimento de álgebras; Dimensão de Gelfand-Kirillov; Gelfand-Kirillov dimension; Growth of algebras; Noncommutative algebra

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APA (6^th Edition):

Galvão, L. (2014). A dimensão de Gelfand-Kirillov de certas álgebras. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/ ;

Chicago Manual of Style (16^th Edition):

Galvão, Lucas. “A dimensão de Gelfand-Kirillov de certas álgebras.” 2014. Masters Thesis, University of São Paulo. Accessed January 24, 2021. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/ ;.

MLA Handbook (7^th Edition):

Galvão, Lucas. “A dimensão de Gelfand-Kirillov de certas álgebras.” 2014. Web. 24 Jan 2021.

Vancouver:

Galvão L. A dimensão de Gelfand-Kirillov de certas álgebras. [Internet] [Masters thesis]. University of São Paulo; 2014. [cited 2021 Jan 24]. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/ ;.

Council of Science Editors:

Galvão L. A dimensão de Gelfand-Kirillov de certas álgebras. [Masters Thesis]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/ ;

University of Alabama

28. Lu, Lei. Noncommutative spaces from matrix models.

Degree: 2016, University of Alabama

URL: http://purl.lib.ua.edu/149909

► Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commutative spacetime. Such spaces may… (more)

▼ Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commutative spacetime. Such spaces may provide insights into physics close to the Planck scale, where quantum gravity becomes relevant. Although there has been much research in the literature, aspects of these NC spaces need further investigation. In this dissertation, we focus on properties of NC spaces in several different contexts. In particular, we study exact NC spaces which result from solutions to matrix model equations of motion. These spaces are associated with finite-dimensional Lie-algebras. More specifically, they are two-dimensional fuzzy spaces that arise from a three-dimensional Yang-Mills type matrix model, four-dimensional tensor-product fuzzy spaces from a tensorial matrix model, and Snyder algebra from a five-dimensional tensorial matrix model. In the first part of this dissertation, we study two-dimensional NC solutions to matrix equations of motion of extended IKKT-type matrix models in three-space-time dimensions. Perturbations around the NC solutions lead to NC field theories living on a two-dimensional space-time. The commutative limit of the solutions are smooth manifolds which can be associated with closed, open and static two-dimensional cosmologies. One particular solution is a Lorentzian fuzzy sphere, which leads to essentially a fuzzy sphere in the Minkowski space-time. In the commutative limit, this solution leads to an induced metric that does not have a fixed signature, and have a non-constant negative scalar curvature, along with singularities at two fixed latitudes. The singularities are absent in the matrix solution which provides a toy model for resolving the singularities of General relativity. We also discussed the two-dimensional fuzzy de Sitter space-time, which has irreducible representations of su(1,1) Lie-algebra in terms of principal, complementary and discrete series. Field theories on such backgrounds result from perturbations about the solutions. The perturbative analysis requires non-standard Seiberg-Witten maps which depend on the embeddings in the ambient space and the symplectic 2-form. We find interesting properties of the field theories in the commutative limit. For example, stability of the action may require adding symmetry breaking terms to the matrix action, along with a selected range for the matrix coefficients. In the second part of this dissertation, we study higher dimensional fuzzy spaces in a tensorial matrix model, which is a natural generalization to the three-dimensional actions and is valid in any number of space-time dimensions. Four-dimensional tensor product NC spaces can be constructed from two-dimensional NC spaces and may provide a setting for doing four-dimensional NC cosmology. Another solution to the tensorial matrix model equations of motion is the Snyder algebra. A crucial step in exploring NC physics is to understand the structure of the quantized space-time in terms of the group representations of… Advisors/Committee Members: Stern, Allen B., Okada, Nobuchika, Harms, Benjamin, Mankey, Gary, Dixon, Martyn, University of Alabama. Dept. of Physics and Astronomy.

Subjects/Keywords: Electronic Thesis or Dissertation; – thesis; Physics; Theoretical physics; FUZZY SPACE; MATRIX MODEL; NONCOMMUTATIVE GEOMETRY; SNYDER ALGEBRA

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lu, L. (2016). Noncommutative spaces from matrix models. (Thesis). University of Alabama. Retrieved from http://purl.lib.ua.edu/149909

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lu, Lei. “Noncommutative spaces from matrix models.” 2016. Thesis, University of Alabama. Accessed January 24, 2021. http://purl.lib.ua.edu/149909.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lu, Lei. “Noncommutative spaces from matrix models.” 2016. Web. 24 Jan 2021.

Vancouver:

Lu L. Noncommutative spaces from matrix models. [Internet] [Thesis]. University of Alabama; 2016. [cited 2021 Jan 24]. Available from: http://purl.lib.ua.edu/149909.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lu L. Noncommutative spaces from matrix models. [Thesis]. University of Alabama; 2016. Available from: http://purl.lib.ua.edu/149909

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

29. Tan, Qijun. Asymptotically Contained Representations and the Spherical Plancherel Formula.

Degree: 2019, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/16244qut101

► We introduce the notion of asymptotic containment of representations of C^*-algebras. The spectral measure of the ambient representation is closely related to the spectral measure… (more)

Subjects/Keywords: Plancherel formula; representation of semi-simple Lie groups; symplectic geometry; noncommutative geometry; harmonic analysis; C^*-algebra

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tan, Q. (2019). Asymptotically Contained Representations and the Spherical Plancherel Formula. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16244qut101

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tan, Qijun. “Asymptotically Contained Representations and the Spherical Plancherel Formula.” 2019. Thesis, Penn State University. Accessed January 24, 2021. https://submit-etda.libraries.psu.edu/catalog/16244qut101.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tan, Qijun. “Asymptotically Contained Representations and the Spherical Plancherel Formula.” 2019. Web. 24 Jan 2021.

Vancouver:

Tan Q. Asymptotically Contained Representations and the Spherical Plancherel Formula. [Internet] [Thesis]. Penn State University; 2019. [cited 2021 Jan 24]. Available from: https://submit-etda.libraries.psu.edu/catalog/16244qut101.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tan Q. Asymptotically Contained Representations and the Spherical Plancherel Formula. [Thesis]. Penn State University; 2019. Available from: https://submit-etda.libraries.psu.edu/catalog/16244qut101

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of New Mexico

30. Vides Romero, Fredy Antonio. Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori.

Degree: Mathematics & Statistics, 2016, University of New Mexico

URL: http://hdl.handle.net/1928/33060

► In this document we solve some local connectivity problems in matrix representations of the form C(T^N) -> M_n and C(T^N) -> M_n <- C([-1, 1]^N)… (more)

Subjects/Keywords: Matrix homotopy; relative lifting problems; matrix representation; noncommutative semialgebraic sets; K-theory; amenable C*-algebra; joint spectrum.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Vides Romero, F. A. (2016). Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/33060

Chicago Manual of Style (16^th Edition):

Vides Romero, Fredy Antonio. “Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori.” 2016. Doctoral Dissertation, University of New Mexico. Accessed January 24, 2021. http://hdl.handle.net/1928/33060.

MLA Handbook (7^th Edition):

Vides Romero, Fredy Antonio. “Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori.” 2016. Web. 24 Jan 2021.

Vancouver:

Vides Romero FA. Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori. [Internet] [Doctoral dissertation]. University of New Mexico; 2016. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/1928/33060.

Council of Science Editors:

Vides Romero FA. Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori. [Doctoral Dissertation]. University of New Mexico; 2016. Available from: http://hdl.handle.net/1928/33060

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