On the algebra of derivations of some Leibniz algebras

Abstract

Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([-,-]\). 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 \(a,b,c\in L\). We study algebras of derivations of some non–nilpotent Leibniz algebras of low dimensions.