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Title 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
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University/Publisher Universidade Estadual de Campinas
Abstract 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 $\Omega$-algebras, which are graded-prime, over an algebraically closed field are uniquely determined by their graded polynomial identities
Subjects/Keywords Álgebras graduadas; Identidades polinomiais graduadas; Matrizes triangulares superiores; Graded algebras; Graded polynomial identities; Upper triangular matrices
Contributors 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)
Language inglês
Country of Publication br
Record ID oai:repositorio.unicamp.br:REPOSIP/333346
Repository unicamp
Date Indexed 2020-09-09
Issued Date 2018-01-01 00:00:00
Note [] Orientadores: Plamen Emilov Kochloukov, Yuri Bahturin; [] Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica; [degreelevel] Doutorado; [degreediscipline] Matematica; [degreename] Doutor em Matemática; [sponsordocumentnumber] 2013/22.802-1, 2017/11.018-9; [sponsor] FAPESP;

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