Codimension growth of algebras with superautomorphism

Let A be a finite dimensional algebra endowed with a superautomorphism over a field of characteristic zero. In this paper we study the asymptotic behavior of the sequence of phi-codimensions c phi / n(A), n = 1, 2, .... More precisely, we shall prove that limn ->infinity n c phi n(A) always exists and it is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of A. This result gives a positive answer to a conjecture of Amitsur in this setting. In the final part of the paper we characterize the algebras whose exponential growth is bounded by 2. (c) 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).