Leibniz algebras: a brief review of current results

V.A. Chupordia; A.A. Pypka; N.N. Semko; V.S. Yashchuk

doi:10.15330/cmp.11.2.250-257

V.A. Chupordia Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
A.A. Pypka Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine https://orcid.org/0000-0003-0837-5395
N.N. Semko University of the State Fiscal Service of Ukraine, 31 Universitetskaya str., 08205, Irpin, Ukraine https://orcid.org/0000-0003-0123-4872
V.S. Yashchuk Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine

https://doi.org/10.15330/cmp.11.2.250-257

Keywords: Leibniz algebra, cyclic Leibniz algebra, ideal, subideal, contraideal, center, lower (upper) central series, finite-dimensional Leibniz algebra, nilpotent Leibniz algebra, Leibniz T-algebra, anticenter, antinilpotent Leibniz algebra

Published online: 2019-12-31

Abstract

Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[\cdot,\cdot]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity $[[a,b],c]=[a,[b,c]]-[b,[a, c]]$ for all $a,b,c\in L$. This paper is a brief review of some current results, which related to finite-dimensional and infinite-dimensional Leibniz algebras.

Leibniz algebras: a brief review of current results

Abstract

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