Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties

S. M. Ratseev

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 8-16

Résumé

Let $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ be the sequence of proper codimensions of a variety $\mathbf{V}$ of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ is presented, i.e. the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ of any such variety $\mathbf{V}$ grows as a polynomial of some degree $k$, but the sequence $\{\gamma_n(\mathbf{W})\}_{n\ge1}$ of any proper subvariety $\mathbf{W}$ in $\mathbf{V}$ grows as a polynomial of degree strictly less than $k$.