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

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 n δ ( 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 n δ ( 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 n δ ( V ) is greater than two. As a consequence, we find a characterization of the varieties whose corresponding exponential growth is equal to two.