Varieties with at most cubic growth.

Abstract Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c n (V) , n = 1 , 2 , ... , and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x (y z) ≡ 0 such that c n (V) < C n α , with 1 ≤ α < 3 , for some constant C. We prove that if 1 ≤ α < 2 then c n (V) ≤ C 1 n , and if 2 ≤ α < 3 , then c n (V) ≤ C 2 n 2 , for some constants C 1 , C 2. [ABSTRACT FROM AUTHOR]