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∈L. We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.