Codimensions of star-algebras and low exponential growth

Abstract

In this paper we prove that if A is any algebra with involution * satisfying a non trivial polynomial identity, then its sequence of * -codimensions is eventually non decreasing. Furthermore by making use of the * -exponent we reconstruct the only two * -algebras, up to T * -equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.