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This article is cited in 2 scientific papers (total in 2 papers)
Short Communication
Algebra
On the nilpotent Leibniz–Poisson algebras
S. M. Ratseeva, O. I. Cherevatenkob a Ul'yanovsk State University, Ul'yanovsk, Russia
b Ul'yanovsk State Pedagogical University, Ul'yanovsk, Russia
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
In this article Leibniz and Leibniz–Poisson algebras in terms of correctness of different identities are investigated. We also examine varieties of these algebras. Let $K$ be a base field of characteristics zero. It is well known that in this case all information about varieties of linear algebras $V$ contains in its polylinear components $P_n(V)$, $n \in \mathbb{N}$, where $P_n(V)$ is a linear span of polylinear words of $n$ different letters in a free algebra $K(X,V)$. In this article we give algebra constructions that generate class of nilpotent varieties of Leibniz algebras and also algebra constructions that generate class of nilpotent by Leibniz varieties of Leibniz–Poisson algebras with the identity $\{ x_1, x_2 \} \cdot \{x_3, x_4 \} = 0$.
Keywords:
Leibniz algebra, Leibniz–Poisson algebra, variety of algebras.
Original article submitted 06/V/2012 revision submitted – 03/VII/2012
Citation:
S. M. Ratseev, O. I. Cherevatenko, “On the nilpotent Leibniz–Poisson algebras”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 207–211
Linking options:
https://www.mathnet.ru/eng/vsgtu1075 https://www.mathnet.ru/eng/vsgtu/v129/p207
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