On minimal Poisson algebras

We present Poisson algebra constructions on the base of associative algebras and study the relationship between the obtained Poisson algebras and the initial associative algebras. Based on obtained constructions, we present two classes of minimal varieties of Poisson algebras of polynomial growth, i.e., varieties for which the sequence of codimensions grows as a polynomial of degree k, but the sequence of codimensions of any proper subvariety grows as a polynomial whose degree is strictly less than k. Previously the author showed that there are only two varieties of Poisson algebras of almost polynomial growth. In this paper we give a complete description of all subvarieties of these two varieties.