A parte polinomial do crescimento das codimensões de álgebras fundamentais tanto no contexto ordinário como no munido de involução

Abstract

Fundamental algebras have been shown to be extremely relevant in PI-theory. In fact, every finite dimensional algebra, over a field of characteristic zero, is PI-equivalent to a direct product of a finite number of fundamental algebras. In this dissertation, we will study the fundamental algebras and present an interesting characterization of these algebras relating their Kemer index to their parameter. We will also study the asymptotic behavior of the codimension sequence of fundamental algebras and show an explicit formula for calculating the invariant known as the polynomial part of the codimension growth. It is noteworthy that, recently, a similar approach was established in the literature for algebras with involution, which is also the object of study in this text. Furthermore, the results presented here are present, although with different statements and proofs, in the papers [1], [10] and [2].