Varieties with at most cubic growth

JOURNAL OF ALGEBRA

卷:518

Article

Mishchenko, S.¹  Valenti, A.² 

[1] Ulyanovsk State Univ, Dept Appl Math, Ulyanovsk 432970, Russia

[2] Univ Palermo, Dipartirnento Energia Ingn Informaz & Modelli Mat, I-90128 Palermo, Italy

关键词: Varieties;    Codimension growth;   

DOI  :  10.1016/j.jalgebra.2018.09.040

来源: Elsevier

【 摘 要 】

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(yz) equivalent to 0 such that c(n) (V) < C-n(alpha) with 1 <= alpha < 3, for some constant C. We prove that if 1 <= alpha < 2 then c(n) (V) <= C-1n, and if 2 <= alpha < 3, then c(n)(V) <= C(2)n(2), for some constants C-1, C-2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free