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) &lt; C-n(alpha) with 1 &lt;= alpha &lt; 3, for some constant C. We prove that if 1 &lt;= alpha &lt; 2 then c(n) (V) &lt;= C-1n, and if 2 &lt;= alpha &lt; 3, then c(n)(V) &lt;= C(2)n(2), for some constants C-1, C-2.

Mishchenko, S., Valenti, A. (2019). Varieties with at most cubic growth. JOURNAL OF ALGEBRA, 518, 321-342 [10.1016/j.jalgebra.2018.09.040].

### 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(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.
##### Scheda breve Scheda completa Scheda completa (DC)
15-gen-2019
Settore MAT/02 - Algebra
Mishchenko, S., Valenti, A. (2019). Varieties with at most cubic growth. JOURNAL OF ALGEBRA, 518, 321-342 [10.1016/j.jalgebra.2018.09.040].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/356776`