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On non-abelian extensions of Leibniz algebras. (English) Zbl 1427.17044

Summary: 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.

MSC:

17B99 Lie algebras and Lie superalgebras
20K40 Homological and categorical methods for abelian groups
55U15 Chain complexes in algebraic topology
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