On Codimensions of Algebras with Involution

Abstract

Let A be an associative algebra with involution ∗ over a field F of characteristic zero. One associates to A, in a natural way, a numerical sequence cn∗(A), n = 1, 2, …, called the sequence of ∗-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In this paper we focus our attention on cn∗(A), n = 1, 2, …, by presenting some recent results about it.