Leibniz Algebras: a brief review of current results

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

Abstract


Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[\cdot,\cdot]$. Then $L$ is called a \textit{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.

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

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