COMMUTATIVE LEIBNIZ-POISSON ALGEBRAS OF POLYNOMIAL GROWTH

Abstract

In this paper we study commutative Leibniz-Poisson algebras. We prove that a variety of commutative Leibniz-Poisson algebras has either polynomial growth or growth with exponential not less than 2, the field being arbitrary. We prove that every variety of commutative Leibniz-Poisson algebras of polynomial growth over a field of characteristic 0 has a finite basis for its polynomial identities. Also we construct a variety of commutative Leibniz-Poisson algebras with almost polynomial growth.