Siberian Federal University

Let K be an arbitrary field and let A be a K-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions of A. We study varieties of Leibniz-Poisson algebras, whose ideals of identities contain the identity {x, y}·{z, t}=0, we study an interrelation between such varieties and varieties of Leibniz algebras. We show that from any Leibniz algebra L one can construct the Leibniz-Poisson algebra A and the properties of L are close to the properties of A. We show that if the ideal of identities of a Leibniz-Poisson variety V does not contain any Leibniz polynomial identity then V has overexponential growth of the codimensions. We construct a variety of Leibniz-Poisson algebras with almost exponential growth.