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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, Volume 14, Issue 2, Pages 150–155
DOI: https://doi.org/10.18500/1816-9791-2014-14-2-150-155
(Mi isu498)
 

Mathematics

On Poisson customary polynomial identities

S. M. Ratseev

Ulyanovsk State University, 42, Leо Tolstoy str., 432017, Ulyanovsk, Russia
References:
Abstract: 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.
Key words: Poisson algebra, variety of algebras, growth of a variety.
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: S. M. Ratseev, “On Poisson customary polynomial identities”, Izv. Saratov Univ. Math. Mech. Inform., 14:2 (2014), 150–155
Citation in format AMSBIB
\Bibitem{Rat14}
\by S.~M.~Ratseev
\paper On Poisson customary polynomial identities
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 2
\pages 150--155
\mathnet{http://mi.mathnet.ru/isu498}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-2-150-155}
\elib{https://elibrary.ru/item.asp?id=21719214}
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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