Leonid A. Kurdachenko, Nikolaj N. Semko, Igor Ya. Subbotin, “On the anticommutativity in Leibniz algebras”, Algebra Discrete Math., 2018, Volume 26, Issue 1,Pages <nobr>97

This article is cited in 3 papers

RESEARCH ARTICLE

On the anticommutativity in Leibniz algebras

Leonid A. Kurdachenko^a, Nikolaj N. Semko^b, Igor Ya. Subbotin^c

^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.

MSC: 17A32, 17A60, 17A99

Received: 12.09.2018

Language: English