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Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 97–109 (Mi adm673)  

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.

Full text: PDF file (350 kB)
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MSC: 17A32, 17A60, 17A99
Received: 12.09.2018
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Citation: Leonid A. Kurdachenko, Nikolaj N. Semko, Igor Ya. Subbotin, “On the anticommutativity in Leibniz algebras”, Algebra Discrete Math., 26:1 (2018), 97–109

Citation in format AMSBIB
\Bibitem{KurSemSub18}
\by Leonid~A.~Kurdachenko, Nikolaj~N.~Semko, Igor~Ya.~Subbotin
\paper On the anticommutativity in Leibniz algebras
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 1
\pages 97--109
\mathnet{http://mi.mathnet.ru/adm673}


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