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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 2(35), Pages 9–15 (Mi vsgtu1298)  

Algebra

On Leibniz–Poisson Special Polynomial Identities

S. M. Ratseeva, O. I. Cherevatenkob

a Ulyanovsk State University, Ulyanovsk, 432017, Russian Federation
b Ulyanovsk State I. N. Ulyanov Pedagogical University, Ulyanovsk, 432063, Russian Federation

Abstract: In this paper we study Leibniz–Poisson algebras satisfying polynomial identities. We study Leibniz–Poisson special and Leibniz–Poisson extended special polynomials. We show that the sequence of codimensions $\{r_n({\mathbf V})\}_{n\geq 1}$ of every extended special space of variety ${\mathbf V}$ of Leibniz-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 $r_n({\mathbf V}) = R(n)$ for all sufficiently large n. It follows that there exists no variety of Leibniz-Poisson algebras with intermediate growth of the sequence $\{r_n({\mathbf V})\}_{n\geq 1}$ between polynomial and exponential. We present lower and upper bounds for the polynomials $R(x)$ of an arbitrary fixed degree.

Keywords: Leibniz algebra, Leibniz–Poisson algebra, variety of algebras
Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1298

Full text: PDF file (620 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 512.572
MSC: 17A32, 17B63
Original article submitted 19/II/2014
revision submitted – 17/III/2014

Citation: S. M. Ratseev, O. I. Cherevatenko, “On Leibniz–Poisson Special Polynomial Identities”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(35) (2014), 9–15

Citation in format AMSBIB
\Bibitem{RatChe14}
\by S.~M.~Ratseev, O.~I.~Cherevatenko
\paper On Leibniz--Poisson Special Polynomial Identities
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 2(35)
\pages 9--15
\mathnet{http://mi.mathnet.ru/vsgtu1298}
\crossref{https://doi.org/10.14498/vsgtu1298}
\zmath{https://zbmath.org/?q=an:06968870}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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