On the algebra of derivations of some low-dimensional 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 the algebras of derivations of nilpotent Leibniz algebras of low dimensions.