subject:(Graded algebras)

Queen Mary, University of London

1. Sutton, Louise. Graded representations of Khovanov-Lauda-Rouquier algebras.

Degree: PhD, 2017, Queen Mary, University of London

URL: http://qmro.qmul.ac.uk/xmlui/handle/123456789/30948 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.766047

► The Khovanov{Lauda{Rouquier algebras Rn are a relatively new family of Z-graded algebras. Their cyclotomic quotients R n are intimately connected to a smaller family of… (more)

▼ The Khovanov{Lauda{Rouquier algebras Rn are a relatively new family of Z-graded algebras. Their cyclotomic quotients R n are intimately connected to a smaller family of algebras, the cyclotomic Hecke algebras H n of type A, via Brundan and Kleshchev's Graded Isomorphism Theorem. The study of representation theory of H n is well developed, partly inspired by the remaining open questions about the modular representations of the symmetric group Sn. There is a profound interplay between the representations for Sn and combinatorics, whereby each irreducible representation in characteristic zero can be realised as a Specht module whose basis is constructed from combinatorial objects. For R n , we can similarly construct their representations as analogous Specht modules in a combinatorial fashion. Many results can be lifted through the Graded Isomorphism Theorem from the symmetric group algebras, and more so from H n , to the cyclotomic Khovanov{Lauda{Rouquier algebras, providing a foundation for the representation theory of R n . Following the introduction of R n , Brundan, Kleshchev and Wang discovered that Specht modules over R n have Z-graded bases, giving rise to the study of graded Specht modules. In this thesis we solely study graded Specht modules and their irreducible quotients for R n . One of the main problems in graded representation theory of R n , the Graded Decomposition Number Problem, is to determine the graded multiplicities of graded irreducible R n -modules arising as graded composition factors of graded Specht modules. We rst consider R n in level one, which is isomorphic to the Iwahori{Hecke algebra of type A, and research graded Specht modules labelled by hook partitions in this context. In quantum characteristic two, we extend to R n a result of Murphy for the symmetric groups, determining graded ltrations of Specht modules labelled by hook partitions, whose factors appear as Specht modules labelled by two-part partitions. In quantum characteristic at least three, we determine an analogous R n -version of Peel's Theorem for the symmetric groups, providing an alternative approach to Chuang, Miyachi and Tan. We then study graded Specht modules labelled by hook bipartitions for R n in level two, which is isomorphic to the Iwahori{Hecke algebra of type B. In quantum characterisitic at least three, we completely determine the composition factors of Specht modules labelled by hook bipartitions for R n , together with their graded analogues.

Subjects/Keywords: Khovanov-Lauda-Rouquier algebras; Z-graded algebras

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APA (6^th Edition):

Sutton, L. (2017). Graded representations of Khovanov-Lauda-Rouquier algebras. (Doctoral Dissertation). Queen Mary, University of London. Retrieved from http://qmro.qmul.ac.uk/xmlui/handle/123456789/30948 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.766047

Chicago Manual of Style (16^th Edition):

Sutton, Louise. “Graded representations of Khovanov-Lauda-Rouquier algebras.” 2017. Doctoral Dissertation, Queen Mary, University of London. Accessed January 26, 2021. http://qmro.qmul.ac.uk/xmlui/handle/123456789/30948 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.766047.

MLA Handbook (7^th Edition):

Sutton, Louise. “Graded representations of Khovanov-Lauda-Rouquier algebras.” 2017. Web. 26 Jan 2021.

Vancouver:

Sutton L. Graded representations of Khovanov-Lauda-Rouquier algebras. [Internet] [Doctoral dissertation]. Queen Mary, University of London; 2017. [cited 2021 Jan 26]. Available from: http://qmro.qmul.ac.uk/xmlui/handle/123456789/30948 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.766047.

Council of Science Editors:

Sutton L. Graded representations of Khovanov-Lauda-Rouquier algebras. [Doctoral Dissertation]. Queen Mary, University of London; 2017. Available from: http://qmro.qmul.ac.uk/xmlui/handle/123456789/30948 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.766047

University of Georgia

2. Turbow, Maren Kathaleen. Structure theory of graded central simple algebras.

Degree: 2017, University of Georgia

URL: http://hdl.handle.net/10724/36718

► This work is focused on the structure theory of graded central simple algebras. We consider algebras graded by Z/pqZ where p and q are distinct… (more)

Subjects/Keywords: Non-Commutative Algebra; Central Simple Algebras; Graded Algebras; Graded Central Simple Algebras; Brauer Group; Graded Brauer Group

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APA (6^th Edition):

Turbow, M. K. (2017). Structure theory of graded central simple algebras. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/36718

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):

Turbow, Maren Kathaleen. “Structure theory of graded central simple algebras.” 2017. Thesis, University of Georgia. Accessed January 26, 2021. http://hdl.handle.net/10724/36718.

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

MLA Handbook (7^th Edition):

Turbow, Maren Kathaleen. “Structure theory of graded central simple algebras.” 2017. Web. 26 Jan 2021.

Vancouver:

Turbow MK. Structure theory of graded central simple algebras. [Internet] [Thesis]. University of Georgia; 2017. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10724/36718.

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

Council of Science Editors:

Turbow MK. Structure theory of graded central simple algebras. [Thesis]. University of Georgia; 2017. Available from: http://hdl.handle.net/10724/36718

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

Universidade Estadual de Campinas

3. Bernardo, Leomaques Francisco Silva, 1985-. Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products.

Degree: 2018, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333581

► Abstract: In this thesis we study graded identities and graded central polynomials for some important algebras over fields of characteristic zero. First we exhibit the… (more)

Subjects/Keywords: Álgebras graduadas; Identidades polinomiais graduadas; Polinômios centrais graduados; Produtos tensoriais; Graded algebras; Graded polynomial identities; Graded central polynomials; Tensor products

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APA (6^th Edition):

Bernardo, Leomaques Francisco Silva, 1. (2018). Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/333581

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):

Bernardo, Leomaques Francisco Silva, 1985-. “Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products.” 2018. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/333581.

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

MLA Handbook (7^th Edition):

Bernardo, Leomaques Francisco Silva, 1985-. “Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products.” 2018. Web. 26 Jan 2021.

Vancouver:

Bernardo, Leomaques Francisco Silva 1. Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products. [Internet] [Thesis]. Universidade Estadual de Campinas; 2018. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333581.

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

Council of Science Editors:

Bernardo, Leomaques Francisco Silva 1. Identidades e polinômios centrais graduados para as álgebras $M_{p,q}(E)$ e seus produtos tensoriais: Identities and graded central polynomials for the algebras $M_{p,q}(E)$ and their tensor products. [Thesis]. Universidade Estadual de Campinas; 2018. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333581

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

University of Utah

4. Trahan, Benjamin. Functors for genuine representations of the metaplectic group and graded affine hecke algebras.

Degree: PhD, Mathematics, 2011, University of Utah

URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/561/rec/1082

► In a recent pre-print, Ciubotaru and Trapa defi ned a family of exact functors carrying spherical Harish-Chandra modules for real classical linear algebraic groups to… (more)

Subjects/Keywords: Graded affine Hecke algebras; Hecke algebras; Lefschetz principle; Metaplectic group; Representation theory

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APA (6^th Edition):

Trahan, B. (2011). Functors for genuine representations of the metaplectic group and graded affine hecke algebras. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/561/rec/1082

Chicago Manual of Style (16^th Edition):

Trahan, Benjamin. “Functors for genuine representations of the metaplectic group and graded affine hecke algebras.” 2011. Doctoral Dissertation, University of Utah. Accessed January 26, 2021. http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/561/rec/1082.

MLA Handbook (7^th Edition):

Trahan, Benjamin. “Functors for genuine representations of the metaplectic group and graded affine hecke algebras.” 2011. Web. 26 Jan 2021.

Vancouver:

Trahan B. Functors for genuine representations of the metaplectic group and graded affine hecke algebras. [Internet] [Doctoral dissertation]. University of Utah; 2011. [cited 2021 Jan 26]. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/561/rec/1082.

Council of Science Editors:

Trahan B. Functors for genuine representations of the metaplectic group and graded affine hecke algebras. [Doctoral Dissertation]. University of Utah; 2011. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/561/rec/1082

University of Illinois – Chicago

5. Bayindir, Haldun Ozgur. Topological Equivalences of E-infinity Differential Graded Algebras.

Degree: 2018, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/23145

► Two DGAs are said to be topologically equivalent when the corresponding Eilenberg–Mac Lane ring spectra are weakly equivalent as ring spectra. Quasi-isomorphic DGAs are topologically… (more)

Subjects/Keywords: Dyer-Lashof operations; Differential graded algebras; Commutative ring spectra; Obstruction theory

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

APA (6^th Edition):

Bayindir, H. O. (2018). Topological Equivalences of E-infinity Differential Graded Algebras. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23145

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):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Thesis, University of Illinois – Chicago. Accessed January 26, 2021. http://hdl.handle.net/10027/23145.

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

MLA Handbook (7^th Edition):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Web. 26 Jan 2021.

Vancouver:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10027/23145.

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

Council of Science Editors:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/23145

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

University of Minnesota

6. Patrias, Rebecca. Combinatorial constructions motivated by K-theory of Grassmannians.

Degree: PhD, Mathematics, 2016, University of Minnesota

URL: http://hdl.handle.net/11299/182175

► Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that… (more)

Subjects/Keywords: dual graded graphs; Hopf algebras; K-theory; symmetric functions

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APA (6^th Edition):

Patrias, R. (2016). Combinatorial constructions motivated by K-theory of Grassmannians. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/182175

Chicago Manual of Style (16^th Edition):

Patrias, Rebecca. “Combinatorial constructions motivated by K-theory of Grassmannians.” 2016. Doctoral Dissertation, University of Minnesota. Accessed January 26, 2021. http://hdl.handle.net/11299/182175.

MLA Handbook (7^th Edition):

Patrias, Rebecca. “Combinatorial constructions motivated by K-theory of Grassmannians.” 2016. Web. 26 Jan 2021.

Vancouver:

Patrias R. Combinatorial constructions motivated by K-theory of Grassmannians. [Internet] [Doctoral dissertation]. University of Minnesota; 2016. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/11299/182175.

Council of Science Editors:

Patrias R. Combinatorial constructions motivated by K-theory of Grassmannians. [Doctoral Dissertation]. University of Minnesota; 2016. Available from: http://hdl.handle.net/11299/182175

7. Yasumura, Felipe Yukihide, 1991-. Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais.

Degree: 2018, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333346

► Abstract: In this thesis, we classify group gradings on the algebra of upper triangular matrices, viewed as Lie and Jordan algebras, over an arbitrary field… (more)

Subjects/Keywords: Álgebras graduadas; Identidades polinomiais graduadas; Matrizes triangulares superiores; Graded algebras; Graded polynomial identities; Upper triangular matrices

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

APA (6^th Edition):

Yasumura, Felipe Yukihide, 1. (2018). Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/333346

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):

Yasumura, Felipe Yukihide, 1991-. “Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais.” 2018. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/333346.

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

MLA Handbook (7^th Edition):

Yasumura, Felipe Yukihide, 1991-. “Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais.” 2018. Web. 26 Jan 2021.

Vancouver:

Yasumura, Felipe Yukihide 1. Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais. [Internet] [Thesis]. Universidade Estadual de Campinas; 2018. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333346.

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

Council of Science Editors:

Yasumura, Felipe Yukihide 1. Group gradings on triangular matrices and graded identities of universal algebras : Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais: Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais. [Thesis]. Universidade Estadual de Campinas; 2018. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/333346

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

Kansas State University

8. Shklyarov, Dmytro. Hirzebruch-Riemann-Roch theorem for differential graded algebras.

Degree: PhD, Department of Mathematics, 2009, Kansas State University

URL: http://hdl.handle.net/2097/1381

► Recall the classical Riemann-Roch theorem for curves: Given a smooth projective complex curve and two holomorphic vector bundles E, F on it, the Euler can… (more)

▼ Recall the classical Riemann-Roch theorem for curves: Given a smooth projective complex curve and two holomorphic vector bundles E, F on it, the Euler can be computed in terms of the ranks and the degrees of the vector bundles. Remarkably, there are a number of similarly looking formulas in algebra. The simplest example is the Ringel formula in the theory of quivers. It expresses the Euler form of two finite-dimensional representations of a quiver algebra in terms of a certain pairing of their dimension vectors. The existence of Riemann-Roch type formulas in these two settings is a consequence of a deeper similarity in the structure of the corresponding derived categories - those of sheaves on curves and of modules over quiver algebras. The thesis is devoted to a version of the Riemann-Roch formula for abstract derived categories. By the latter we understand the derived categories of differential graded (DG) categories. More specifically, we work with the categories of perfect modules over DG algebras. These are a simultaneous generalization of the derived categories of modules over associative algebras and the derived categories of schemes. Given an arbitrary DG algebra A, satisfying a certain finiteness condition, we define and explicitly describe a canonical pairing on its Hochschild homology. Then we give an explicit formula for the Euler character of an arbitrary perfect A-module, the character is an element of the Hochschild homology of A. In this setting, our noncommutative Riemann-Roch formula expresses the Euler characteristic of the Hom-complex between any two perfect A-modules in terms of the pairing of their Euler characters. One of the main applications of our results is a theorem that the aforementioned pairing on the Hochschild homology is non-degenerate when the DG algebra satisfies a smoothness condition. This theorem implies a special case of the well-known noncommutative Hodge-to-de Rham degeneration conjecture. Another application is related to mathematical physics: We explicitly construct an open-closed topological field theory from an arbitrary Frobenius algebra and then, following ideas of physicists, interpret the noncommutative Riemann-Roch formula as a special case of the so-called topological Cardy condition. Advisors/Committee Members: Yan S. Soibelman.

Subjects/Keywords: Differential graded algebras; Differential graded categories; Mathematics (0405)

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

APA (6^th Edition):

Shklyarov, D. (2009). Hirzebruch-Riemann-Roch theorem for differential graded algebras. (Doctoral Dissertation). Kansas State University. Retrieved from http://hdl.handle.net/2097/1381

Chicago Manual of Style (16^th Edition):

Shklyarov, Dmytro. “Hirzebruch-Riemann-Roch theorem for differential graded algebras.” 2009. Doctoral Dissertation, Kansas State University. Accessed January 26, 2021. http://hdl.handle.net/2097/1381.

MLA Handbook (7^th Edition):

Shklyarov, Dmytro. “Hirzebruch-Riemann-Roch theorem for differential graded algebras.” 2009. Web. 26 Jan 2021.

Vancouver:

Shklyarov D. Hirzebruch-Riemann-Roch theorem for differential graded algebras. [Internet] [Doctoral dissertation]. Kansas State University; 2009. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2097/1381.

Council of Science Editors:

Shklyarov D. Hirzebruch-Riemann-Roch theorem for differential graded algebras. [Doctoral Dissertation]. Kansas State University; 2009. Available from: http://hdl.handle.net/2097/1381

Universidade Estadual de Campinas

9. Biânchi, Angelo Calil, 1984-. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.

Degree: 2012, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031

► Abstract: This work is dedicated to the study of some aspects of the representation theory of certain algebras which can be regarded as generalizations of… (more)

Subjects/Keywords: Kac-Moody, Algebras de; Representações de álgebras; Fórmulas de caracteres; Álgebras graduadas; Kac-Moody algebras; Representations of algebras; Hyperalgebras; Character formulas; Graded algebras

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

APA (6^th Edition):

Biânchi, Angelo Calil, 1. (2012). Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031

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):

Biânchi, Angelo Calil, 1984-. “Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.” 2012. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031.

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

MLA Handbook (7^th Edition):

Biânchi, Angelo Calil, 1984-. “Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.” 2012. Web. 26 Jan 2021.

Vancouver:

Biânchi, Angelo Calil 1. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031.

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

Council of Science Editors:

Biânchi, Angelo Calil 1. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031

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

10. Ozbek, Aydin. The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology.

Degree: 2019, University of Nevada – Reno

URL: http://hdl.handle.net/11714/5732

► Building on the seminal works of Quillen and Sullivan, Bousfield and Guggenheim developed a "homotopy theory" for commutative differential graded algebras (cdgas) in order to… (more)

Subjects/Keywords: brown category; commutative differential graded algebras; Homotopy Theory; Lie algebra cohomology; representability

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APA (6^th Edition):

Ozbek, A. (2019). The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology. (Thesis). University of Nevada – Reno. Retrieved from http://hdl.handle.net/11714/5732

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):

Ozbek, Aydin. “The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology.” 2019. Thesis, University of Nevada – Reno. Accessed January 26, 2021. http://hdl.handle.net/11714/5732.

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

MLA Handbook (7^th Edition):

Ozbek, Aydin. “The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology.” 2019. Web. 26 Jan 2021.

Vancouver:

Ozbek A. The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology. [Internet] [Thesis]. University of Nevada – Reno; 2019. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/11714/5732.

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

Council of Science Editors:

Ozbek A. The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology. [Thesis]. University of Nevada – Reno; 2019. Available from: http://hdl.handle.net/11714/5732

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

Université de Grenoble

11. Langlois, Kevin. Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one.

Degree: Docteur es, Mathématiques, 2013, Université de Grenoble

URL: http://www.theses.fr/2013GRENM068

►

Cette thèse est consacrée aux propriétés géométriques des opérations de tores algébriques dans les variétés affines. Elle est issue de trois prépublications qui correspondent aux… (more)

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Cette thèse est consacrée aux propriétés géométriques des opérations de tores algébriques dans les variétés affines. Elle est issue de trois prépublications qui correspondent aux points (1), (2), (3) ci-après. Soit X une variété affine munie d’une opération d’un tore algébrique T. Nous appelons complexité la codimension de l’orbite générale de T dans X. Sous l’hypothèse de normalité et lorsque le corps de base est algébriquement clos de caractéristique 0, la variété X admet une description combinatoire en termes de géométrie convexe. Cette description, obtenue en 2006 par Altmann et Hausen, généralise celle classique des variétes toriques. Notre but consiste à étudier des problèmes nouveaux concernant les propriétés algébriques et géométriques de X lorsque l’operation de T dans X est de complexité 1. (1) Dans la première partie, un résultat donne une manière explicite de déterminer la clôture intégrale de toute variété affine définie sur un corps algébriquement clos de caractérisque 0 munie d’une opération de T de complexité 1 en termes de la description combinatoire d’Altmann-Hausen. Comme application, nous donnons une classification complète des idéaux intégralement clos homogènes de l’algèbre des fonctions régulières de X et généralisons un théorème de Reid-Roberts-Vitulli sur la description de certains idéaux normaux de l’algèbre des polynômes à plusieurs variables. (2) Les calculs de la première partie suggèrent une démonstration de la validité de la présentation d’Altmann-Hausen sur un corps quelconque dans le cas de complexité 1. Ce qui est fait dans la deuxième partie. Dans la situation non déployée, la descente galoisienne d’une variété affine normale munie d’une opération d’un tore algébrique de complexité 1 est décrite par un nouvel objet combinatoire que nous appelons diviseur polyédral Galois stable. (3) Dans la troisième partie, lorsque que le corps de base est parfait, nous classifions toutes les opérations du groupe additif dans X normalisées par l’action de T de complexité 1. Cette classification généralise des travaux classiques de Flenner et Zaidenberg dans le cas des surfaces et de Liendo dans le cas où le corps ambiant est algébriquement clos de caractéristique 0.

This thesis is devoted to the study of geometric properties of affine algebraic varieties endowed with an action of an algebraic torus. It comes from three preprints which correspond to the indicated points (1), (2), (3). Let X be an affine variety equipped with an action of the algebraic torus T. The complexity of the T-action on X is the codimension of the general T-orbit. Under the assumption of normality and when the ground field is algebraically closed of characteristic 0, the variety X admits a combinatorial description in terms of convex geometry. This description obtained by Altmann and Hausen in the year 2006 generalizes the classical one for toric varieties. Our purpose is to investigate new problems on the algebraic and geometric properties of the variety X when the T-action on X is of complexity 1. (1) In the first part,…

Advisors/Committee Members: Zaidenberg, Mikhail (thesis director).

Subjects/Keywords: Variétés algébriques affines; Groupes algébriques; Géométrie convexe; Algèbres graduées; Affine algebraic varieties; Algebraic groups; Convex geometry; Graded algebras; 510

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

APA (6^th Edition):

Langlois, K. (2013). Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2013GRENM068

Chicago Manual of Style (16^th Edition):

Langlois, Kevin. “Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one.” 2013. Doctoral Dissertation, Université de Grenoble. Accessed January 26, 2021. http://www.theses.fr/2013GRENM068.

MLA Handbook (7^th Edition):

Langlois, Kevin. “Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one.” 2013. Web. 26 Jan 2021.

Vancouver:

Langlois K. Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one. [Internet] [Doctoral dissertation]. Université de Grenoble; 2013. [cited 2021 Jan 26]. Available from: http://www.theses.fr/2013GRENM068.

Council of Science Editors:

Langlois K. Sur les opérations de tores algébriques de complexité un dans les variétés affines : On affine varieties with an algebraic torus action of complexity one. [Doctoral Dissertation]. Université de Grenoble; 2013. Available from: http://www.theses.fr/2013GRENM068

Universidade de Brasília

12. Evander Pereira de Rezende. Identidades polinomiais graduadas de algumas àlgebras matriciais.

Degree: 2010, Universidade de Brasília

URL: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=6879

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Let K be an associative and commutative ring with 1 and let A be an associative Kalgebra with or without 1. We say that the… (more)

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Let K be an associative and commutative ring with 1 and let A be an associative Kalgebra with or without 1. We say that the polynomial identities of A have the Specht property if each K-algebra B satisfying all the polynomial identities of A has a finite basis for its identities. Let M2(K) be the algebra of 2 × 2 matrices over a field K. If K is a field of characteristic 0 then, by the celebrated result of Kemer, the polynomial identities of every algebra over K have the Specht property. In particular, the result holds for the polynomial identities of M2(K). However, if the characteristic of the field K is positive and K is infinite, it is not known if the identities of M2(K) have such a property . In this work we study the Specht property for the 2-graded polynomial identities of the algebra M2(K) over an associative and commutative Noetherian ring with 1. The 2-grading of M2(K) is given by M2(K)0 = {(a 0 ) a, d K} , M2(K)1 = {(0 b); b, c K}. {(0 d); {(c 0) Our main result is as follows: Let K be an associative and commutative Noetherian ring with 1. Then the 2- graded polynomial identities of the algebra M2(K) of 2 × 2 matrices over K have the Specht property. We have proved also the Specht property for the graded polynomial identities of some other algebras.

Seja K um anel associativo, comutativo e unitário e seja A uma K- álgebra associativa com ou sem 1. Dizemos que as identidades polinomiais de A possuem a propriedade de Specht se qualquer K- álgebra B satisfazendo todas as identidades polinomiais de A possui base finita para suas identidades. Seja M2(K) a álgebra de matrizes 2 × 2 sobre um corpo K. Se K for um corpo de característica 0, então, pelo celebrado resultado de Kemer, as identidades polinomiais de toda álgebra sobre K têm a propriedade de Specht. Em particular, vale o resultado para as identidades de M2(K). Entretanto, se a característica do corpo K é positiva e K é infinito, não é conhecido se as identidades de M2(K) possuem tal propriedade. Neste trabalho estudamos a propriedade de Specht para as identidades polinomiais 2-graduadas da álgebra M2(K) sobre um anel K associativo, comutativo, Noetheriano e unitário. A 2-graduação de M2(K) é dada por M2(K)0 = {(a 0 ) a, d K} , M2(K)1 = {(0 b); b, c K}. {(0 d); {(c 0) Nosso resultado principal é o seguinte: Seja K um anel associativo, comutativo e Noetheriano com 1. Então as identidades polinomiais 2-graduadas da álgebra M2(K) de matrizes 2 × 2 sobre K possuem a propriedade de Specht. Mostramos a propriedade de Specht também para as identidades polinomiais graduadas de algumas outras álgebras.

Advisors/Committee Members: Shirlei Serconek, José Antônio Oliveira de Freitas, Irina Sviridova, Ivan Chestakov, Alexei Krassilnikov.

Subjects/Keywords: identidades polinomiais; pi-àlgebras, propriedade da base finita; propriedade de specht; àlgebras matriciais; specht property; Algebras graduadas; pi-algebras; matrix álgebras; ALGEBRA; Graded álgebras; polynomial identities; finite basis Property

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

APA (6^th Edition):

Rezende, E. P. d. (2010). Identidades polinomiais graduadas de algumas àlgebras matriciais. (Thesis). Universidade de Brasília. Retrieved from http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=6879

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):

Rezende, Evander Pereira de. “Identidades polinomiais graduadas de algumas àlgebras matriciais.” 2010. Thesis, Universidade de Brasília. Accessed January 26, 2021. http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=6879.

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

MLA Handbook (7^th Edition):

Rezende, Evander Pereira de. “Identidades polinomiais graduadas de algumas àlgebras matriciais.” 2010. Web. 26 Jan 2021.

Vancouver:

Rezende EPd. Identidades polinomiais graduadas de algumas àlgebras matriciais. [Internet] [Thesis]. Universidade de Brasília; 2010. [cited 2021 Jan 26]. Available from: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=6879.

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

Council of Science Editors:

Rezende EPd. Identidades polinomiais graduadas de algumas àlgebras matriciais. [Thesis]. Universidade de Brasília; 2010. Available from: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=6879

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

13. Sánchez, Jesús. About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres.

Degree: Docteur es, Mathématiques. Topologie algébrique, 2016, Sorbonne Paris Cité

URL: http://www.theses.fr/2016USPCC204

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Dans cette thèse nous rappelons la notion de L-algèbre, qui a pour objet d'être un modèle algébrique des types d'homotopie. L'objectif principal de cette thèse… (more)

Subjects/Keywords: Modules différentiels gradués; L-algèbres; Opérades symétriques; E-infini-coalgèbres; L-algèbre; Differential graded modules; L-algebras; Symmetric operads; E-infinity coalgebras; L-algebras

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

APA (6^th Edition):

Sánchez, J. (2016). About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres. (Doctoral Dissertation). Sorbonne Paris Cité. Retrieved from http://www.theses.fr/2016USPCC204

Chicago Manual of Style (16^th Edition):

Sánchez, Jesús. “About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres.” 2016. Doctoral Dissertation, Sorbonne Paris Cité. Accessed January 26, 2021. http://www.theses.fr/2016USPCC204.

MLA Handbook (7^th Edition):

Sánchez, Jesús. “About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres.” 2016. Web. 26 Jan 2021.

Vancouver:

Sánchez J. About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres. [Internet] [Doctoral dissertation]. Sorbonne Paris Cité; 2016. [cited 2021 Jan 26]. Available from: http://www.theses.fr/2016USPCC204.

Council of Science Editors:

Sánchez J. About E-infinity-structures in L-algebras : Sur les E-infini-structures dans les L-algèbres. [Doctoral Dissertation]. Sorbonne Paris Cité; 2016. Available from: http://www.theses.fr/2016USPCC204

Georgia State University

14. Malec, Sara. Noetherian Filtrations and Finite Intersection Algebras.

Degree: MS, Mathematics and Statistics, 2008, Georgia State University

URL: https://scholarworks.gsu.edu/math_theses/55

► This paper presents the theory of Noetherian filtrations, an important concept in commutative algebra. The paper describes many aspects of the theory of these objects,… (more)

Subjects/Keywords: intersection algebras; E.P.F. filtrations; Rees algebras; Noetherian filtrations; graded rings and modules; Mathematics

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

APA (6^th Edition):

Malec, S. (2008). Noetherian Filtrations and Finite Intersection Algebras. (Thesis). Georgia State University. Retrieved from https://scholarworks.gsu.edu/math_theses/55

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):

Malec, Sara. “Noetherian Filtrations and Finite Intersection Algebras.” 2008. Thesis, Georgia State University. Accessed January 26, 2021. https://scholarworks.gsu.edu/math_theses/55.

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

MLA Handbook (7^th Edition):

Malec, Sara. “Noetherian Filtrations and Finite Intersection Algebras.” 2008. Web. 26 Jan 2021.

Vancouver:

Malec S. Noetherian Filtrations and Finite Intersection Algebras. [Internet] [Thesis]. Georgia State University; 2008. [cited 2021 Jan 26]. Available from: https://scholarworks.gsu.edu/math_theses/55.

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

Council of Science Editors:

Malec S. Noetherian Filtrations and Finite Intersection Algebras. [Thesis]. Georgia State University; 2008. Available from: https://scholarworks.gsu.edu/math_theses/55

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

15. Plyley, Chris. Polynomial Identities on Algebras with Actions.

Degree: 2014, University of Western Ontario

URL: https://ir.lib.uwo.ca/etd/2399

► When an algebra is endowed with the additional structure of an action or a grading, one can often make striking conclusions about the algebra based… (more)

▼ When an algebra is endowed with the additional structure of an action or a grading, one can often make striking conclusions about the algebra based on the properties of the structure-induced subspaces. For example, if A is an associative G-graded algebra such that the homogeneous component A1 satisfies an identity of degree d, then Bergen and Cohen showed that A is itself a PI-algebra. Bahturin, Giambruno and Riley later used combinatorial methods to show that the degree of the identity satisfied by A is bounded above by a function of d and |G|. Utilizing a similar approach, we prove an analogue of this result which applies to associative algebras whose induced Lie or Jordan algebras are G-graded. Group-gradings and actions by a group of automorphisms are examples of Hopf algebras acting on H-algebras. If H is finite-dimensional, semisimple, commutative, and splits over its base field, then it is known that A is an H-algebra precisely when the H-action on A induces a certain group-grading of A. We extend this duality to incorporate other natural H-actions. To this end, we introduce the notion of an oriented H-algebra. For example, if A has an action by a group of both automorphisms and anti-automorphisms, then A is not an H-algebra, but A is an oriented H-algebra. The vector space gradings associated to oriented H-algebra actions are not generally group-gradings, or even set-gradings. However, when A is a Lie algebra, the grading is a quasigroup-grading, and, when A is an associative algebra, the grading is what we call a Lie-Jordan-grading. Lastly, we call certain H-polynomials in the free associative H-algebra essential, and show that, if an (associative) H-algebra A satisfies an essential H-identity of degree d, then A satisfies an ordinary identity of bounded degree. Furthermore, in the case when H is m-dimensional, semisimple and commutative, we prove that, if AH satisfies an ordinary identity of degree d, then A satisfies an essential H-identity of degree dm. From this we are able to recover several well-known results as special cases.

Subjects/Keywords: Noncommutative Algebra; Polynomial Identity Algebras; Graded Algebras; Hopf Algebras; Anti-automorphisms; Algebra

…background information about polynomial identity theory and graded algebras. We outline some of the… …Polynomial Identities and Graded Algebras This chapter is meant to provide the reader with an… …we discuss group-graded algebras, and we define some other types of gradings that are… …Graded Algebras Definition 2.1.1. Let X = {x1 , x2 , . . .} , let f (x1… …Identities and Graded Algebras In some sense, PI-algebras which satisfy smaller degree polynomials…

1 more image…

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

APA (6^th Edition):

Plyley, C. (2014). Polynomial Identities on Algebras with Actions. (Thesis). University of Western Ontario. Retrieved from https://ir.lib.uwo.ca/etd/2399

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):

Plyley, Chris. “Polynomial Identities on Algebras with Actions.” 2014. Thesis, University of Western Ontario. Accessed January 26, 2021. https://ir.lib.uwo.ca/etd/2399.

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

MLA Handbook (7^th Edition):

Plyley, Chris. “Polynomial Identities on Algebras with Actions.” 2014. Web. 26 Jan 2021.

Vancouver:

Plyley C. Polynomial Identities on Algebras with Actions. [Internet] [Thesis]. University of Western Ontario; 2014. [cited 2021 Jan 26]. Available from: https://ir.lib.uwo.ca/etd/2399.

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

Council of Science Editors:

Plyley C. Polynomial Identities on Algebras with Actions. [Thesis]. University of Western Ontario; 2014. Available from: https://ir.lib.uwo.ca/etd/2399

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

Universidade Estadual de Campinas

16. Reis, Júlio César dos, 1979-. Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra.

Degree: 2012, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363

► Abstract: In this PhD thesis we give bases of the graded polynomial identities of...Note: The complete abstract is available with the full electronic document Advisors/Committee… (more)

Subjects/Keywords: PI-álgebras; Identidade polinomial; Aneís graduados; Matrizes (Matemática); Corpos finitos (Álgebra); PI-algebras; Polynomial identity; Graded rings; Matrix algebra; Finite fields (Algebra)

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

APA (6^th Edition):

Reis, Júlio César dos, 1. (2012). Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363

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):

Reis, Júlio César dos, 1979-. “Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra.” 2012. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363.

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

MLA Handbook (7^th Edition):

Reis, Júlio César dos, 1979-. “Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra.” 2012. Web. 26 Jan 2021.

Vancouver:

Reis, Júlio César dos 1. Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363.

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

Council of Science Editors:

Reis, Júlio César dos 1. Graduações e identidades graduadas para álgebras de matrizes: Gradings and graded identities for matrix algebra. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363

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

Universidade Estadual de Campinas

17. Ferreira, Mauricio de Araujo, 1982-. Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras.

Degree: 2011, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563

► Abstract: In this thesis work we study the connection between two theories of noncommutative valuation: Dubrovin valuation rings and gauges. Dubrovin valuation rings were introduced… (more)

▼ Abstract: In this thesis work we study the connection between two theories of noncommutative valuation: Dubrovin valuation rings and gauges. Dubrovin valuation rings were introduced in 1982 as a generalization of invariant valuation rings to Artinian simple rings. Gauges are valuation-like maps that can be defined not only on division algebras, but more generally, on finite-dimensional semisimple algebras over valued fields. Gauges were introduced much more recently in 2010 by Tignol and Wadsworth. Just as for valuations on fields, we can define a ring associated to a gauge, which we call gauge ring. Arithmetic properties of the gauge ring are studied. We show that the gauge ring is always a semi-local order integral over its center. We also describe the gauge ring with respect to composition of gauges and scalar extension. We introduce the concept of minimal gauge on central simple algebras, which are gauges that the degree zero part of the associated graded ring has the least number of simple components. We show that the ring of a minimal gauge is an intersection of a family of Dubrovin valuation rings having the intersection property. The intersection property was introduced by Gräter in 1992. We also proved that if we start with a family of Dubrovin valuation rings having the intersection property, then there exist a minimal gauge associated, assuming that the valuation of the center has finite rank. In this direction, our main result is an existence theorem of minimal gauges on central simple algebra over a field with a finite rank valuation. We also generalize for simple algebras, non-necessarily central, a result of Tignol and Wadsworth which relate gauges with certain value functions introduced by Morandi in 1989. This value functions are associated to Dubrovin valuation rings integral over its center. As a consequence of this last result, we obtain an existence theorem of gauges on finite dimensional semisimple algebras over a field with a rank one valuation Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Engler, Antonio José, 1944- (advisor), Wadsworth, Adrian Roscoe (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Marcos, Eduardo do Nascimento (committee member), Ferrero, Miguel Angel Alberto (committee member), Moura, Adriano Adrega de (committee member), Brumatti, Paulo Roberto (committee member).

Subjects/Keywords: Teoria da valorização; Aneis de divisão; Álgebras associativas; Aneís graduados; Anéis de valorização de Dubrovin; Valuation theory; Division rings; Associative algebras; Graded rings; Dubrovin valuation rings

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

APA (6^th Edition):

Ferreira, Mauricio de Araujo, 1. (2011). Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563

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):

Ferreira, Mauricio de Araujo, 1982-. “Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras.” 2011. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563.

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

MLA Handbook (7^th Edition):

Ferreira, Mauricio de Araujo, 1982-. “Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras.” 2011. Web. 26 Jan 2021.

Vancouver:

Ferreira, Mauricio de Araujo 1. Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras. [Internet] [Thesis]. Universidade Estadual de Campinas; 2011. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563.

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

Council of Science Editors:

Ferreira, Mauricio de Araujo 1. Funções valorização e anéis de valorização de Dubrovin em álgebras simples: Value functions and Dubrovin valuation rings on simple algebras. [Thesis]. Universidade Estadual de Campinas; 2011. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306563

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

18. RODRIGUEZ REY, ANDRES. Combinatorial Hopf Algebras and Dual graded graphs .

Degree: 2016, Universidad de los Andes

URL: https://documentodegrado.uniandes.edu.co/documentos/8182.pdf

► Siendo la generalización de la noción de grupo, las álgegras de Hopf son una estructura algebraica de gran importancia que aparece en varias áreas de… (more)

Subjects/Keywords: Combinatoria; Álgebras de Hopf; Combinatorics; Hopf Algebras; Dual graded graphs; Algebraic Combinatorics.

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

APA (6^th Edition):

RODRIGUEZ REY, A. (2016). Combinatorial Hopf Algebras and Dual graded graphs . (Thesis). Universidad de los Andes. Retrieved from https://documentodegrado.uniandes.edu.co/documentos/8182.pdf

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):

RODRIGUEZ REY, ANDRES. “Combinatorial Hopf Algebras and Dual graded graphs .” 2016. Thesis, Universidad de los Andes. Accessed January 26, 2021. https://documentodegrado.uniandes.edu.co/documentos/8182.pdf.

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

MLA Handbook (7^th Edition):

RODRIGUEZ REY, ANDRES. “Combinatorial Hopf Algebras and Dual graded graphs .” 2016. Web. 26 Jan 2021.

Vancouver:

RODRIGUEZ REY A. Combinatorial Hopf Algebras and Dual graded graphs . [Internet] [Thesis]. Universidad de los Andes; 2016. [cited 2021 Jan 26]. Available from: https://documentodegrado.uniandes.edu.co/documentos/8182.pdf.

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

Council of Science Editors:

RODRIGUEZ REY A. Combinatorial Hopf Algebras and Dual graded graphs . [Thesis]. Universidad de los Andes; 2016. Available from: https://documentodegrado.uniandes.edu.co/documentos/8182.pdf

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

Georgia Southern University

19. Nelson, Michael S. Homological Constructions over a Ring of Characteristic 2.

Degree: MSin Mathematics (M.S.), Department of Mathematical Sciences, 2019, Georgia Southern University

URL: https://digitalcommons.georgiasouthern.edu/etd/1960

► We study various homological constructions over a ring R of characteristic 2. We construct chain complexes over a field K of characteristic 2 using… (more)

Subjects/Keywords: Classification of differential graded algebras; Characteristic 2; Homological algebra; Chain complexes; Simplicial complexes; Gröbner basis; Algebra; Jack N. Averitt College of Graduate Studies, Electronic Theses & Dissertations, ETDs, Student Research

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APA (6^th Edition):

Nelson, M. S. (2019). Homological Constructions over a Ring of Characteristic 2. (Masters Thesis). Georgia Southern University. Retrieved from https://digitalcommons.georgiasouthern.edu/etd/1960

Chicago Manual of Style (16^th Edition):

Nelson, Michael S. “Homological Constructions over a Ring of Characteristic 2.” 2019. Masters Thesis, Georgia Southern University. Accessed January 26, 2021. https://digitalcommons.georgiasouthern.edu/etd/1960.

MLA Handbook (7^th Edition):

Nelson, Michael S. “Homological Constructions over a Ring of Characteristic 2.” 2019. Web. 26 Jan 2021.

Vancouver:

Nelson MS. Homological Constructions over a Ring of Characteristic 2. [Internet] [Masters thesis]. Georgia Southern University; 2019. [cited 2021 Jan 26]. Available from: https://digitalcommons.georgiasouthern.edu/etd/1960.

Council of Science Editors:

Nelson MS. Homological Constructions over a Ring of Characteristic 2. [Masters Thesis]. Georgia Southern University; 2019. Available from: https://digitalcommons.georgiasouthern.edu/etd/1960

University of Oregon

20. Nash, David A., 1982-. Graded representation theory of Hecke algebras.

Degree: 2010, University of Oregon

URL: http://hdl.handle.net/1794/10871

► We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at… (more)

Subjects/Keywords: Symmetric groups; Specht modules; Irreducible representation; Graded representation; Hecke algebras; Mathematics; Theoretical mathematics

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APA (6^th Edition):

Nash, David A., 1. (2010). Graded representation theory of Hecke algebras. (Thesis). University of Oregon. Retrieved from http://hdl.handle.net/1794/10871

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):

Nash, David A., 1982-. “Graded representation theory of Hecke algebras.” 2010. Thesis, University of Oregon. Accessed January 26, 2021. http://hdl.handle.net/1794/10871.

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

MLA Handbook (7^th Edition):

Nash, David A., 1982-. “Graded representation theory of Hecke algebras.” 2010. Web. 26 Jan 2021.

Vancouver:

Nash, David A. 1. Graded representation theory of Hecke algebras. [Internet] [Thesis]. University of Oregon; 2010. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1794/10871.

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

Council of Science Editors:

Nash, David A. 1. Graded representation theory of Hecke algebras. [Thesis]. University of Oregon; 2010. Available from: http://hdl.handle.net/1794/10871

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

Universidade Estadual de Campinas

21. Souza, Manuela da Silva, 1985-. Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2.

Degree: 2013, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362

► Abstract: The abstract is available with the full electronic document Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Kochloukov, Plamen Emilov, 1958-… (more)

Subjects/Keywords: Álgebras não-associativas; PI-álgebras; Lie, Álgebra de; Identidade polinomial graduada; Nonassociative algebras; PI-algebras; Lie algebra; Graded polynomial identity

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APA (6^th Edition):

Souza, Manuela da Silva, 1. (2013). Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362

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):

Souza, Manuela da Silva, 1985-. “Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2.” 2013. Thesis, Universidade Estadual de Campinas. Accessed January 26, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362.

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

MLA Handbook (7^th Edition):

Souza, Manuela da Silva, 1985-. “Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2.” 2013. Web. 26 Jan 2021.

Vancouver:

Souza, Manuela da Silva 1. Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2. [Internet] [Thesis]. Universidade Estadual de Campinas; 2013. [cited 2021 Jan 26]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362.

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

Council of Science Editors:

Souza, Manuela da Silva 1. Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2: Specht property and growth of the graded polynomial identities of sl_2. [Thesis]. Universidade Estadual de Campinas; 2013. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362

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

University of Oregon

22. Phan, Christopher Lee, 1980-. Koszul and generalized Koszul properties for noncommutative graded algebras.

Degree: 2009, University of Oregon

URL: http://hdl.handle.net/1794/10367

► We investigate some homological properties of graded algebras. If A is an R -algebra, then E (A) := Ext A ( R, R ) is… (more)

Subjects/Keywords: Koszul properties; Noncommutative graded algebras; Yoneda algebra; Grobner bases; Homological algebra; Mathematics; Algebra, Homological; Algebra, Yoneda; Koszul algebras

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APA (6^th Edition):

Phan, Christopher Lee, 1. (2009). Koszul and generalized Koszul properties for noncommutative graded algebras. (Thesis). University of Oregon. Retrieved from http://hdl.handle.net/1794/10367

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):

Phan, Christopher Lee, 1980-. “Koszul and generalized Koszul properties for noncommutative graded algebras.” 2009. Thesis, University of Oregon. Accessed January 26, 2021. http://hdl.handle.net/1794/10367.

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

MLA Handbook (7^th Edition):

Phan, Christopher Lee, 1980-. “Koszul and generalized Koszul properties for noncommutative graded algebras.” 2009. Web. 26 Jan 2021.

Vancouver:

Phan, Christopher Lee 1. Koszul and generalized Koszul properties for noncommutative graded algebras. [Internet] [Thesis]. University of Oregon; 2009. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1794/10367.

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

Council of Science Editors:

Phan, Christopher Lee 1. Koszul and generalized Koszul properties for noncommutative graded algebras. [Thesis]. University of Oregon; 2009. Available from: http://hdl.handle.net/1794/10367

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

Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

23. Κανάκογλου, Κωνσταντίνος. Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική.

Degree: 2008, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)

URL: http://hdl.handle.net/10442/hedi/19353

►

The subject of this thesis is the algebraic study of parafermionic and parabosonic algebras and especially the determination of the various Hopf structures possibly present… (more)

▼

The subject of this thesis is the algebraic study of parafermionic and parabosonic algebras and especially the determination of the various Hopf structures possibly present in them together with indications of possible applications in physics. In chapter 2, an historical introduction is presented together with the first important results regarding the representations of these algebras, in the language they were first stated by Green, Greenberg and Messiah. The rest of the thesis consists of two parts: · Chapter 3, which constitutes a self-contained mathematical introduction into various topics related to the Hopf algebra theory. · Chapters 4,5,6 in which the original results of the thesis are presented: In chapter 4, we lay down the definitions of bosonic and parabosonic algebras in a modern algebraic language and we prove these algebras to be Z2-gr. algebras. The bosonic algebra is also proved to be a quotient algebra of the parabosonic algebra. We show that the notion of Z2 grading is equivalent to a specific action of the Z2 group and we proceed to computing this action. We then proceed to presenting a graded description of the Fock and the Fock-like representations. Finally the parabosonic algebra is proved to be a graded Hopf algebra (or equivalently a braided group). In chapter 5, consequences of the graded Hopf structure are extensively studied: The Green ansatz algebras are shown to be isomorphic to graded tensor products of the bosonic algebra and some progress is made towards a braided construction of the parabosonic Fock-like representations. Some novel generalizations of the Green ansatz are also presented. Finally, the notion of braided group is studied and two methods (one bibliography-based and the second totally new) are presented with the aim of which ordinary Hopf structures for the parabosonic algebra are constructed. A discussion on the comparison of the methods and their results is also supplied. In chapter 6, we contruct realizations of Lie algebras and Lie superalgebras (in both the finite and infinite dim. case) using either parabosonic and parafermionic algebras or mixed algebras which combine parabosonic and parafermionic degrees of freedom. The role played by the various Hopf structures in these realizations together with possible applications in physics and in representation theory are extensively discussed.

Το αντικείμενο της διατριβής είναι η αλγεβρική μελέτη των παραφερμιονικών και παραμποζονικών αλγεβρών και πιο συγκεκριμένα η μελέτη των πιθανών Hopf δομών που εμφανίζουν οι άλγεβρες αυτές καθώς και οι πιθανές εφαρμογές στη φυσική. Στο κεφ. 2 παρουσιάζεται μια ιστορική εισαγωγή αλλά και τα πρώτα σημαντικά αποτελέσματα σχετικά με τις αναπαραστάσεις των αλγεβρών αυτών όπως πρωτοδιατυπώθηκαν από τους Green, Greenberg, Messiah. Το υπόλοιπο της διατριβής αποτελείται από δύο τμήματα: · Το κεφ. 3, το οποίο αποτελεί μια αυτόνομη μαθηματική εισαγωγή στις έννοιες των Hopf αλγεβρών. · Τα κεφ. 4,5,6 τα οποία παρουσιάζουν τα πρωτότυπα ερευνητικά αποτελέσματα της διατριβής: Στο κεφ.…

Subjects/Keywords: Παραμποζόνια; Παραφερμόνια; Hopf άλγεβρες; Αναπαραστάσεις; Βαθμωτές άλγεβρες; Lie άλγεβρες; Lie βαθμωτές άλγεβρες; Green ansatz; Parabosons; Parafermions; Hopf algebras; Representations; Graded algebras; Lie algebras; Lie suteralgebras

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APA (6^th Edition):

Κανάκογλου, . �. (2008). Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική. (Thesis). Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/19353

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):

Κανάκογλου, Κωνσταντίνος. “Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική.” 2008. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed January 26, 2021. http://hdl.handle.net/10442/hedi/19353.

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

MLA Handbook (7^th Edition):

Κανάκογλου, Κωνσταντίνος. “Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική.” 2008. Web. 26 Jan 2021.

Vancouver:

Κανάκογλου �. Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2008. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10442/hedi/19353.

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

Council of Science Editors:

Κανάκογλου �. Δομή Hopf στις παραφερμιονικές και παραμποζονικές άλγεβρες και εφαρμογές των αλγεβρών αυτών στη φυσική. [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2008. Available from: http://hdl.handle.net/10442/hedi/19353

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

24. Covolo, Tiffany. (Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie.

Degree: Docteur es, Mathématiques, 2014, Université Claude Bernard – Lyon I

URL: http://www.theses.fr/2014LYO10203

►

La présente thèse porte sur le développement d'une théorie d'algèbre linéaire, de géométrie et d'analyse basée sur les algèbres (Z2)n-commutatives, c'est-à-dire des algèbres (Z2)n-graduées associatives… (more)

▼

La présente thèse porte sur le développement d'une théorie d'algèbre linéaire, de géométrie et d'analyse basée sur les algèbres (Z2)n-commutatives, c'est-à-dire des algèbres (Z2)n-graduées associatives unitaires satisfaisant ab = (-1)<deg(a),deg(b)>ba, pour tout couple d'éléments homogènes a, b de degrés deg(a), deg(b) où <.,.> est le produit scalaire usuel). Cette généralisation de la supergéométrie a de nombreuses applications : en mathématiques (l'algèbre de Deligne des superformes différentielles, l'algèbre des quaternions et les algèbres de Clifford en sont des exemples) et même en physique (paraparticules). Dans ce travail, les notions de trace et de (super)déterminant pour des matrices à coefficients dans une algèbre gradué-commutative sont définies et étudiés. Une attention particulière est portée au cas des algèbres de Clifford : ce point de vue gradué fournit une nouvelle approche au problème classique du « bon » déterminant pour des matrices à coefficient non-commutatifs (quaternioniques). En outre, nous entreprenons l'étude de la géométrie différentielle (Z2)n-graduée. Privilégiant l'approche par les espaces annelés, les (Z2)n-supervariétés sont définies en choisissant l'algèbre (Z2)n-commutative des séries formelles en variables graduées comme modèle pour le faisceau de fonctions. Les résultats les plus marquants ainsi obtenus sont : le Berezinien gradué et son interprétation cohomologique (essentielle pour établir une théorie de l'intégration) ; le théorème des morphismes, attestant qu'on peut rétablir un morphisme entre (Z2)n-supervariétés à partir de sa seule expression sur les coordonnées ; le théorème de Batchelor-Gawedzki pour les (Z2)n-supervariétés lisses

The present thesis deals with a development of linear algebra, geometry and analysis based on (Z2)n-superalgebras ; associative unital algebras which are (Z2)n-graded and graded-commutative, i.e. statisfying ab=(-1)<deg(a),deg(b)>ba, for all homogeneous elements a, b of respective degrees deg(a), deg(b) in (Z2)n (<.,.> denoting the usual scalar product). This generalization widens the range of applications of supergeometry to many mathematical structures (quaternions and more generally Clifford algebras, Deligne algebra of superdifferential forms, higher vector bundles) and appears also in physics (for describing paraparticles) proving its worth and relevance. In this dissertation, we first focus on (Z2)n-superalgebra theory ; we define and characterize the notions of trace and (super)determinant of matrices over graded-commutative algebras. Special attention is given to the case of Clifford algebras, where our study gives a new approach to treat the classical problem of finding a “good” determinant for matrices with noncommuting (quaternionic) entries. Further, we undertake the study of (Z2)n-graded differential geometry. Privileging the ringed space approach, we define (smooth) (Z2)n-supermanifolds modeling their algebras of functions on the (Z2)n-commutative algebra of formal power series in graded variables, and develop the theory along…

Advisors/Committee Members: Ovsienko, Valentin (thesis director), Poncin, Norbert (thesis director).

Subjects/Keywords: Superalgèbre; Algèbre graduée-commutative; Trace et Bérézinien; Algèbres de Clifford; Déterminant quaternionique; Supergéometrie; Séries formelles; Double fibré vectoriel; Superalgebra; Graded-commutative algebra; Trace and Berezinian; Clifford algebras; Quaternionic determinants; Higher supergeometry; Formal power series; Higher vector bundles; 512

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

APA (6^th Edition):

Covolo, T. (2014). (Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie. (Doctoral Dissertation). Université Claude Bernard – Lyon I. Retrieved from http://www.theses.fr/2014LYO10203

Chicago Manual of Style (16^th Edition):

Covolo, Tiffany. “(Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie.” 2014. Doctoral Dissertation, Université Claude Bernard – Lyon I. Accessed January 26, 2021. http://www.theses.fr/2014LYO10203.

MLA Handbook (7^th Edition):

Covolo, Tiffany. “(Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie.” 2014. Web. 26 Jan 2021.

Vancouver:

Covolo T. (Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie. [Internet] [Doctoral dissertation]. Université Claude Bernard – Lyon I; 2014. [cited 2021 Jan 26]. Available from: http://www.theses.fr/2014LYO10203.

Council of Science Editors:

Covolo T. (Z2)n-Superalgebra and (Z2)n-Supergeometry : (Z2)n-Superalgèbre and (Z2)n-Supergéométrie. [Doctoral Dissertation]. Université Claude Bernard – Lyon I; 2014. Available from: http://www.theses.fr/2014LYO10203

25. Wilson, Kevin Hayes. Three perspectives on n points in P^{n-2} .

Degree: PhD, 2013, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp018k71nh131

► This thesis is divided into three parts, each focused on extending the work of Bhargava's Higher Composition Laws and his asymptotics of the density of… (more)

▼ This thesis is divided into three parts, each focused on extending the work of Bhargava's Higher Composition Laws and his asymptotics of the density of discriminants. The first part is focused on the gemoetry of numbers methods of . In this part, we prove asymptotics for the class number times the regulator of cubic fields and orders, and for the square of the same for quadratic fields and orders. This requires extending Bhargava's methods to prehomogeneous vector spaces with a positive-dimensional generic isotropy group. The second part focuses on more traditional analytic methods. In it, we demonstrate that the values L(1, k) for k an S₃-cubic or S₄-quartic number field behave like random Euler products, extending work of Barban and Eliott from the quadratic case. More generally, we show that the same holds if k is replaced by an order in such a field. Conditional on the Strong Artin Conjecture for Galois representations \Gal(\Bar{\Q}/\Q) → \GL_n-1(\C) with image S_n and what we call the Strong Malle Conjecture for S_n number fields, we prove that L(1, k) behaves like a random Euler product for k an S_n number field for any n ≥ 2. In the final part, we turn to putting Bhargava's Higher Composition Laws in a more commutative algebraic context. In particular, taking inspriation from a letter of Deligne to Bhargava and Wood's thesis, we produce a canonical associative, commutaive, differential graded algebra structures on the minimal free resolutions of n general points in \bP^n-2_\Q. We believe our method is novel, relying on the representation theory of the symmetric group. In our penultimate chapter, we show that this method extends to produce canonical multiplicative structures on other free resolutions associated to the representation theory of the symmetric group. Of particular interest is that all of the resolutions we produce are pure and do not appear to arise from the so-called tensor complexes of Berkesch, Erman, Kummini, and Sam. Finally, in the last chapter, we briefly discuss the representation theoretic import of the sextic resolvent of a quintic field. At this time, we have not been able to use this to extend Bhargava's parameterization of quintic rings to arbitrary base schemes in the spirit of Deligne and Wood, but we believe that this chapter forms an important start in that direction. Advisors/Committee Members: Bhargava, Manjul (advisor).

Subjects/Keywords: density theorems; differential graded algebras; number fields; random euler products; symmetric group

…space is Gorenstein. 1.3.7 Differential Graded Algebras Suppose then that F• is a complex… …reader. 1.2.1 (Graded) Rings Unless otherwise specified, all rings are associative… …commutative, unital, and noetherian. A ring R is said to be graded if • there is a ring R0 such that… …rank r. Then R[x1 , . . . , xr ] = Sym• V is a graded R module with the usual… …multiplication structure of polynomials. Unless otherwise specified, by graded ring we will mean…

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

APA (6^th Edition):

Wilson, K. H. (2013). Three perspectives on n points in P^{n-2} . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp018k71nh131

Chicago Manual of Style (16^th Edition):

Wilson, Kevin Hayes. “Three perspectives on n points in P^{n-2} .” 2013. Doctoral Dissertation, Princeton University. Accessed January 26, 2021. http://arks.princeton.edu/ark:/88435/dsp018k71nh131.

MLA Handbook (7^th Edition):

Wilson, Kevin Hayes. “Three perspectives on n points in P^{n-2} .” 2013. Web. 26 Jan 2021.

Vancouver:

Wilson KH. Three perspectives on n points in P^{n-2} . [Internet] [Doctoral dissertation]. Princeton University; 2013. [cited 2021 Jan 26]. Available from: http://arks.princeton.edu/ark:/88435/dsp018k71nh131.

Council of Science Editors:

Wilson KH. Three perspectives on n points in P^{n-2} . [Doctoral Dissertation]. Princeton University; 2013. Available from: http://arks.princeton.edu/ark:/88435/dsp018k71nh131

ETH Zürich

26. Knus, Max-Albert. Sur une classe d'algèbres filtrées.

Degree: 1967, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/135466

Subjects/Keywords: ASSOZIATIVE RINGE UND ASSOZIATIVE ALGEBREN (ALGEBRA); GRADUIERTE ALGEBREN (ALGEBRA); FILTRIERUNGEN (HOMOLOGISCHE ALGEBRA); ASSOCIATIVE RINGS AND ASSOCIATIVE ALGEBRAS (ALGEBRA); GRADED ALGEBRAS (ALGEBRA); FILTRATIONS (HOMOLOGICAL ALGEBRA); info:eu-repo/classification/ddc/510; Mathematics

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

APA (6^th Edition):

Knus, M. (1967). Sur une classe d'algèbres filtrées. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/135466

Chicago Manual of Style (16^th Edition):

Knus, Max-Albert. “Sur une classe d'algèbres filtrées.” 1967. Doctoral Dissertation, ETH Zürich. Accessed January 26, 2021. http://hdl.handle.net/20.500.11850/135466.

MLA Handbook (7^th Edition):

Knus, Max-Albert. “Sur une classe d'algèbres filtrées.” 1967. Web. 26 Jan 2021.

Vancouver:

Knus M. Sur une classe d'algèbres filtrées. [Internet] [Doctoral dissertation]. ETH Zürich; 1967. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/20.500.11850/135466.

Council of Science Editors:

Knus M. Sur une classe d'algèbres filtrées. [Doctoral Dissertation]. ETH Zürich; 1967. Available from: http://hdl.handle.net/20.500.11850/135466

ETH Zürich

27. Willwacher, Thomas. Cyclic formality.

Degree: 2009, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/151769

Subjects/Keywords: ZYKLISCHE KOHOMOLOGIE (ALGEBRAISCHE GEOMETRIE); GRADUIERTE ALGEBREN (ALGEBRA); LIE-RINGE UND LIE-ALGEBREN (ALGEBRA); DIFFERENTIALOPERATOREN + INTEGRALOPERATOREN AUF MANNIGFALTIGKEITEN (TOPOLOGIE); CYCLIC COHOMOLOGY (ALGEBRAIC GEOMETRY); GRADED ALGEBRAS (ALGEBRA); LIE RINGS AND LIE ALGEBRAS (ALGEBRA); DIFFERENTIAL + INTEGRAL OPERATORS ON MANIFOLDS (TOPOLOGY); info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; Mathematics; Mathematics

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

APA (6^th Edition):

Willwacher, T. (2009). Cyclic formality. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/151769

Chicago Manual of Style (16^th Edition):

Willwacher, Thomas. “Cyclic formality.” 2009. Doctoral Dissertation, ETH Zürich. Accessed January 26, 2021. http://hdl.handle.net/20.500.11850/151769.

MLA Handbook (7^th Edition):

Willwacher, Thomas. “Cyclic formality.” 2009. Web. 26 Jan 2021.

Vancouver:

Willwacher T. Cyclic formality. [Internet] [Doctoral dissertation]. ETH Zürich; 2009. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/20.500.11850/151769.

Council of Science Editors:

Willwacher T. Cyclic formality. [Doctoral Dissertation]. ETH Zürich; 2009. Available from: http://hdl.handle.net/20.500.11850/151769

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