PI-equivalência em álgebras graduadas simples
This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we will show the following: Let G be a group, F an algebraically closed eld, and R =...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Brasil |
| Recursos: | Universidade Federal de São Carlos (UFSCAR) |
| Repositorio: | Repositório Institucional da UFSCAR |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/7911 |
| Acesso em linha: | https://repositorio.ufscar.br/handle/20.500.14289/7911 |
| Access Level: | acceso abierto |
| Palavra-chave: | PI- álgebras G-graduações Identidades polinomiais Identidades graduadas Álgebras graduadas simples G-gradings Polynomial identities Graded identities Graded simple algebras CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA |
| Resumo: | This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we will show the following: Let G be a group, F an algebraically closed eld, and R = L g2G Rg a finite dimensional G-graded F-algebra such that the order of each finite subgroup of G is invertible in F. Then R is a G-graded simple algebra if and only if R is isomorphic, as graded algebra, to the tensor product C = Mn(F) F [H], where H is a nite subgroup of G, is a 2-cocycle in H, Mn(F) has an elementary G-grading, F [H] has a canonical grading and C has an induced G-grading by the tensor product. Based on this result, admitting the same assumptions and adding that G is an abelian group, we prove that two graded simple algebras satisfy the same graded identities if and only if they are isomorphic as graded algebras. |
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