Crescimento polinomial das codimensões e *-codimensões

Abstract

Let F be a field of characteristic zero. We say that the sequence of codimensions of an algebra A is polynomially bounded if there exist constants and t such that cn(A) nt for all n 1: In this dissertation, we will study the polynomial growth of codimensions and *-codimensions, based on the articles of Giambruno - Zaicev and of Giambruno - Mishchenko on the subject. Our main goal is to give an interesting description of the algebras (and algebras with involution *, respectively)with polynomial growth of codimensions (*-codimensions, respectively) in the language of cocharacters (*-cocharacters, respectively). For this, we will exploit the theories of representations of the symmetric group Sn and of the hyperoctahedral group Z2 o Sn. Furthermore, we will see that, under some hypotheses, the algebras with polynomial growth of codimensions can be decomposed into appropriate finite-dimensional subalgebras.