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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2012, Issue 4(29), Pages 207–211
DOI: https://doi.org/10.14498/vsgtu1075
(Mi vsgtu1075)
 

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
Full-text PDF (142 kB) Citations (2)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
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
Bibliographic databases:
Document Type: Article
UDC: 512.572
MSC: Primary 17A32; Secondary 17B63
Language: Russian
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
Citation in format AMSBIB
\Bibitem{RatChe12}
\by S.~M.~Ratseev, O.~I.~Cherevatenko
\paper On the nilpotent Leibniz--Poisson algebras
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 4(29)
\pages 207--211
\mathnet{http://mi.mathnet.ru/vsgtu1075}
\crossref{https://doi.org/10.14498/vsgtu1075}
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  • https://www.mathnet.ru/eng/vsgtu/v129/p207
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Abstract page:430
    Full-text PDF :181
    References:38
    First page:1
     
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