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Mathematics
On Poisson customary polynomial identities
S. M. Ratseev Ulyanovsk State University, 42, Leо Tolstoy str., 432017, Ulyanovsk, Russia
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.
Citation:
S. M. Ratseev, “On Poisson customary polynomial identities”, Izv. Saratov Univ. Math. Mech. Inform., 14:2 (2014), 150–155
Linking options:
https://www.mathnet.ru/eng/isu498 https://www.mathnet.ru/eng/isu/v14/i2/p150
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Abstract page: | 187 | Full-text PDF : | 74 | References: | 48 |
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