Proper T-ideals of poisson algebras with extreme properties

Abstract

Let {γn(V)}_n≥1 be the sequence of proper codimensions of some variety V of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence {γn(V)}_n≥1 is presented, i.e., the sequence {γn(V)}_n≥1 of any such variety V grows as a polynomial of some degree k, but the sequence {γn(W)}_n≥1 of any proper subvariety W in V grows as a polynomial of degree strictly less than k.