Geodesic
On Leibniz--Poisson Special Polynomial Identities
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 9-15

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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, variety of algebras.
Mots-clés : Leibniz–Poisson algebra 
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     author = {S. M. Ratseev and O. I. Cherevatenko},
     title = {On {Leibniz--Poisson} {Special} {Polynomial} {Identities}},
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S. M. Ratseev; O. I. Cherevatenko. On Leibniz--Poisson Special Polynomial Identities. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 9-15. http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a18/