Lie-Derivations of Some Nilpotent and Solvable Leibniz Algebras

Abstract

Leibniz algebras are generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. The derivation operator on algebras and their generalizations are important object in non-associative algebras. We have a number of generalizations of derivations, one of which is Lie-derivation. In this work, we investigate Lie-derivations of solvable Leibniz algebras and describe Lie-derivations for some nilpotent Leibniz algebras and lie-derivations of naturally graded filiform Leibniz algebras. Moreover, we give the description of Lie-derivations for three-dimensional nilpotent Leibniz algebras. In addition, the following are defined here: Lie-derivations of solvable Leibniz algebras with filiform and nulfiliform nilradical.