Geodesic
On Poisson customary polynomial identities
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 150-155

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We study Poisson customary and Poisson extended customary polynomials. We show that the sequence of codimensions $\{r_n(V)\}_{n\geq1}$ of every extended customary space of variety $V$ of Poisson algebras over an arbitrary field is either bounded by a polynomial or at least exponential. Furthermore, if this sequence is bounded by polynomial then there is a polynomial $R(x)$ with rational coefficients such that $r_n(V)=R(n)$ for all sufficiently large $n$. We present lower and upper bounds for the polynomials $R(x)$ of an arbitrary fixed degree. 
@article{ISU_2014_14_2_a4,
     author = {S. M. Ratseev},
     title = {On {Poisson} customary polynomial identities},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {150--155},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a4/}
}
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S. M. Ratseev. On Poisson customary polynomial identities. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 150-155. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a4/