Variedades de álgebras G-graduadas com involução graduada de crescimento quase polinomial

• Ano de defesa: 2022
• Autor(a) principal: Lorena Mara Costa Oliveira
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: identidade polinomial; involução graduada; codimensão; crescimento quase polinomial; Matemática – Teses; Identidades polinomiais – Teses; Involução graduada – Teses; Identidades (Matemática) – Teses
• Link de acesso: http://hdl.handle.net/1843/45129

In this thesis, the main object of study is the class of the (G, ∗)-algebras, that is, algebras graded by a group G and endowed with a graded involution ∗. Firstly, we study the algebraic structure of the (G, ∗)-algebras. In this case, we characterize the finite dimensional simple (G, ∗)-algebras over an algebraically closed field of characteristic zero, where G is a finite abelian group. Moreover, we present the classification of the finite dimensional simple (Cp, ∗)-algebras over any algebraically closed field of characteristic zero, for an odd prime p, extending the results given in [4]. After that, we study the class of the (G, ∗)- algebras in the context of the PI-theory. Our main goal is to characterize the varieties of polynomial growth generated by finite dimensional (G, ∗)-algebras, where G is a finite abelian group. As a consequence, we classify all varieties generate by finite dimensional (G, ∗)-algebras of almost polynomial growth.