Codimensions of algebras with pseudoautomorphism and their exponential growth

Abstract

Let F be a fixed field of characteristic zero containing an element i such that $i^2=-1$. In this paper we consider finite dimensional superalgebras over F endowed with a pseudoautomorphism p and we investigate the asymptotic behavior of the corresponding sequence of p-codimensions $c_n^p\left(A\right)$, $n=1,2,\dots$. First we give a positive answer to a conjecture of Amitsur in this setting: the p-exponent ${\exp }^p\left(A\right)={\lim }_{n\to \infty }\sqrt[n]{c_n^p\left(A\right)}$ always exists and it is an integer. In the final part we characterize the algebras whose exponential growth is bounded by 2.