Identidades polinomiais graduadas para a álgebra das matrizes triangulares superiores sobre um corpo finito
Let K be a field of characteristic p and let UTn = UTn(K) be the algebra of n x n upper triangular matrices over K with the usual product a . b of the elements a,b ∈ UTn. In this thesis we describe the set of all G-graded polynomial identities of UTn, where G is any group and K is any finite field....
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| Tipo de documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2021 |
| País: | Brasil |
| Recursos: | Universidade Federal de São Carlos (UFSCAR) |
| Repositório: | Repositório Institucional da UFSCAR |
| Idioma: | português |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/15540 |
| Acesso em linha: | https://repositorio.ufscar.br/handle/20.500.14289/15540 |
| Access Level: | Acceso aberto |
| Palavra-chave: | PI-álgebra Identidades polinomiais graduadas Matrizes triangulares superiores Álgebras de Lie Propriedade de Specht PI-algebra Graded polynomial identities Upper triangular matrices Lie algebras Specht property CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA::GRUPOS DE ALGEBRA NAO-COMUTAVIVA |
| Resumo: | Let K be a field of characteristic p and let UTn = UTn(K) be the algebra of n x n upper triangular matrices over K with the usual product a . b of the elements a,b ∈ UTn. In this thesis we describe the set of all G-graded polynomial identities of UTn, where G is any group and K is any finite field. The vector space UTn with the new product [a,b] = a . b - b . a is a Lie algebra, denoted by UTn^(-). We describe the set of all G-graded polynomial identities of UT2^(-), where G is any abelian group and K is any field with characteristic p ≠ 2. |
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