PI-equivalência em álgebras graduadas simples

• Ano de defesa: 2016
• Autor(a) principal: Naves, Fernando Augusto
• Orientador(a): Talpo, Humberto Luiz
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: PI- álgebras; G-graduações; Identidades polinomiais; Identidades graduadas; Álgebras graduadas simples
• Palavras-chave em Inglês: G-gradings; Polynomial identities; Graded identities; Graded simple algebras
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/7911

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.