Non-abelian extensions of Rota-Baxter pre-Lie algebras and Wells exact sequences

Abstract:

      In this paper, we introduce non-abelian cohomology groups and classify the non-abelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups. Next, we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras. Finally, we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.