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1. 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 and arbitrary grading group. Using this result, and assuming stronger conditions, we were able to obtain the classification of group gradings on the algebra of block-triangular matrices, viewed as Lie and Jordan algebras. We compute the asymptotic behavior of the graded codimension sequence for any grading on the associative algebra of upper-triangular matrices. For the Lie case, we obtain a partial result for the asymptotic behavior of graded codimensions, and we compute the graded exponent of all gradings on the upper triangular matrices, as Lie and Jordan algebras. Finally, we investigate the problem of determining a simple algebra by its polynomial identities. We prove that finite-dimensional graded Ω-algebras, which are graded-prime, over an algebraically closed field are uniquely determined by their graded polynomial identities Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Kochloukov, Plamen Emilov, 1958- (advisor), Bahturin, Yuri (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Di Vincenzo, Onofrio Mario (committee member), Aljadeff, Eli (committee member), La Mattina, Daniela (committee member), Chestakov, Ivan (committee member).

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 (6th 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 (16th 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 March 08, 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 (7th 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. 08 Mar 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 Mar 08]. 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


Universidade Estadual de Campinas

2. Gonçalves, Dimas José. A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras.

Degree: 2009, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369 

Abstract: In this PhD thesis we study polynomial identities in associative algebras. More precisely we study the A-ideIltities for several important classes of algebras. The first main result of the thesis gives a complete description of the A-identities for the Grassmann algebra over an algebraically closed field of characteristic O. In this way we give a positive answer to a conjecture due to Henke and Regev. Afterwards we study A-identities for the upper triangular matrix algebras. We give a lower bound for the minimal degree of an A-identity satisfied by such algebras. As a corollary we give a negative answer to another conjecture due to Henke and Regev. Furthermore we describe the A-identities of degree 5 for the upper triangular matrices of order 2 and compute the minimal degree of an A-identity for such algebras of order 3 and 4. Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Kochloukov, Plamen Emilov, 1958- (advisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Moura, Adriano Adrega de (committee member), Rocco, Norai Romeu (committee member), Krassilnikov, Alexei Nikolaevich (committee member), Coelho, Flavio Ulhoa (committee member).

Subjects/Keywords: Identidade polinomial; A-identidade polinomial; Grassmann, Álgebra de; Matrizes triangulares superiores; PI-álgebras; PI-algebra; Polynomial identity; A-polynomial identity; Grassmann algebra; Upper triangular matrices

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

APA (6th Edition):

Gonçalves, D. J. (2009). A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369

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

Chicago Manual of Style (16th Edition):

Gonçalves, Dimas José. “A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras.” 2009. Thesis, Universidade Estadual de Campinas. Accessed March 08, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369.

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

MLA Handbook (7th Edition):

Gonçalves, Dimas José. “A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras.” 2009. Web. 08 Mar 2021.

Vancouver:

Gonçalves DJ. A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras. [Internet] [Thesis]. Universidade Estadual de Campinas; 2009. [cited 2021 Mar 08]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369.

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

Council of Science Editors:

Gonçalves DJ. A-identidades polinomiais em algebras associativas: A-polynomial identities in associative algebras. [Thesis]. Universidade Estadual de Campinas; 2009. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369

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

.