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Algebra and Discrete Mathematics, 2018, Volume 26, Issue 1, Pages 97–109
(Mi adm673)
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This article is cited in 3 scientific papers (total in 3 papers)
RESEARCH ARTICLE
On the anticommutativity in Leibniz algebras
Leonid A. Kurdachenkoa, Nikolaj N. Semkob, Igor Ya. Subbotinc a Department of Geometry and Algebra, Dnipro National University, 72 Gagarin Av., Dnipro, 49010, Ukraine
b Department of Mathematics, University of State Fiscal Service of Ukraine, Irpin, 09200, Ukraine
c Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA
Abstract:
Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency (Lie nilpotentency).
Keywords:
Leibniz algebra, Lie algebra, center, Lie-center, anticenter, central series, anticentral series, Lie-central series.
Received: 12.09.2018
Citation:
Leonid A. Kurdachenko, Nikolaj N. Semko, Igor Ya. Subbotin, “On the anticommutativity in Leibniz algebras”, Algebra Discrete Math., 26:1 (2018), 97–109
Linking options:
https://www.mathnet.ru/eng/adm673 https://www.mathnet.ru/eng/adm/v26/i1/p97
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Abstract page: | 191 | Full-text PDF : | 47 | References: | 27 |
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