Crossed modules and non-abelian extensions of Rota-Baxter Leibniz algebras

Abstract

We introduce the notions of crossed modules of Rota-Baxter Leibniz algebras, 2-term Rota-Baxter sh Leibniz algebras, and discuss the relationship between them and the 3-th cohomology group of Rota-Baxter Leibniz algebras. We classify the non-abelian extensions by introducing the non-abelian cohomology. Based on this classification, we study the inducibility of a pair of automorphisms about a non-abelian extension of Rota-Baxter Leibniz algebras, and give the fundamental sequence of Wells in the context of Rota-Baxter Leibniz algebras.