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

Abstract

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.