On non-abelian extensions of Leibniz algebras

Abstract

In this paper, we study non-abelian extensions of Leibniz algebras using two different approaches. First we construct two Leibniz 2-algebras using biderivations of Leibniz algebras and show that under a condition on centers, a non-abelian extension of Leibniz algebras can be described by a Leibniz 2-algebra morphism. Furthermore, under this condition, non-abelian extensions are classified by homotopy classes of Leibniz 2-algebra morphisms. Then we give a description of non-abelian extensions of Leibniz algebras in terms of Maurer-Cartan elements in a differential graded Lie algebra.