A characterization of varieties of algebras of proper central exponent greater than two

Abstract

Let F be a field of characteristic zero and let V be a variety of associative F-algebras. In [19] Regev introduced a numerical sequence measuring the growth of the proper central polynomials of a generating algebra of V. Such sequence c delta n(V), n >= 1, is called the sequence of proper central polynomials of V and in [12], [13] the authors computed its exponential growth. This is an invariant of the variety. They also showed that c delta n(V) either grows exponentially or is polynomially bounded. The purpose of this paper is to characterize the varieties of associative algebras whose exponential growth of c delta n(V) is greater than two. As a consequence, we find a characterization of the varieties whose corresponding exponential growth is equal to two. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).