ON THE NILPOTENT LEIBNIZ-POISSON ALGEBRAS

In this article Leibniz and Leibniz-Poisson algebras in terms of correctness of different identities are investigated. We also examine varieties of these algebras. Let K be a base field of characteristics zero. It is well known that in this case all information about varieties of linear algebras V contains in its polylinear components P-n (V), n is an element of N, where P-n (V) is a linear span of polylinear words of n different letters in a free algebra K (X, V). In this article we give algebra constructions that generate class of nilpotent varieties of Leibniz algebras and also algebra constructions that generate class of nilpotent by Leibniz varieties of Leibniz-Poisson algebras with the identity {x(1), x(2)} . {x(3), x(4)} = 0.