Correlation of Poisson algebras and Lie algebras in the language of identities

In the paper, the varieties of Poisson algebras whose ideals of identities contain the identity {x, y}· {z, t} = 0 are studied, and the correlation of these varieties with varieties of Lie algebras is investigated. A variety of Poisson algebras of almost exponential growth is presented. An example of a variety of Poisson algebras with fractional exponent is also given.