Cohomologies, non-abelian extensions and Wells exact sequences of λ-differential pre-Lie algebras

The purpose of the present paper is to study cohomologies and non-abelian extensions of λ-differential pre-Lie algebras. First, we consider representations and cohomologies of λ-differential pre-Lie algebras. Next, we investigate non-abelian extensions and classify the non-abelian extensions in terms of non-abelian cohomology groups. Furthermore, we address the inducibility of a pair of automorphisms on non-abelian extensions and develop the Wells exact sequences in the context of λ-differential pre-Lie algebras. Finally, we discuss these results in the case of abelian extensions of λ-differential pre-Lie algebras.