Proper T-Ideals of Poisson Algebras with Extreme Properties / S. M. Ratseev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 6. P. 8-16 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 224-232].

Let \{\gamma_n({\bf V})\}_{n\geq 1} be the sequence of proper codimensions of some variety {\bf 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({\bf V})\}_{n\geq 1} is presented, i.e., the sequence \{\gamma_n({\bf V})\}_{n\geq 1} of any such variety {\bf V} grows as a polynomial of some degree k, but the sequence \{\gamma_n({\bf W})\}_{n\geq 1} of any proper subvariety {\bf W} in {\bf V} grows as a polynomial of degree strictly less than k.

Key words: Poisson algebra, variety of algebras, growth of a variety.