On the structure of low-dimensional Leibniz algebras: some revision

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 \([[a,b],c]=[a,[b,c]]-[b,[a,c]]\) for all \(a,b,c\in L\). We describe the inner structure of left Leibniz algebras having dimension 3.