S. M. Ratseev, O. I. Cherevatenko, “On metabelian varieties of Leibniz–Poisson algebras”, Bulletin of Irkutsk State University. Series Mathematics, 2013, Volume 6, Issue 1,Pages <nobr>72

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On metabelian varieties of Leibniz–Poisson algebras

S. M. Ratseev^a, O. I. Cherevatenko^b

^a Ulyanovsk State University, 432017, Ulyanovsk, Lev Tolstoy, 42
^b Ulyanovsk State I. N. Ulyanov Pedagogical University, Ploshchad’ 100-letiya so dnya rozhdeniya V. I. Lenina, 4

Abstract: In this paper we give algebra constructions that generate the metabelian variety of Leibniz–Poisson algebras with the identity $\{ x, y \} \cdot \{z, t \} = 0$. We give the asymptotic description of the metabelian varieties.

Keywords: Poisson algebra, Leibniz–Poisson algebra, variety of algebras, growth of variety.

UDC: 512.572