Leonid A. Kurdachenko, Nikolaj N. Semko, Igor Ya. Subbotin, “On the anticommutativity in Leibniz algebras”, Algebra Discrete Math., 2018, том 26, выпуск 1,страницы 97

Эта публикация цитируется в 3 статьях

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

Аннотация: 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).

Ключевые слова: Leibniz algebra, Lie algebra, center, Lie-center, anticenter, central series, anticentral series, Lie-central series.

MSC: 17A32, 17A60, 17A99

Поступила в редакцию: 12.09.2018

Язык публикации: английский