On non-abelian extensions of Rota—Baxter algebras, dendriform algebras and Wells short exact sequence

A Rota—Baxter algebra $A_R$ is an algebra $A$ equipped with a distinguished Rota—Baxter operator $R$ on it. Rota—Baxter algebras are closely related to dendriform algebras introduced by Loday. In this paper, we first consider the non-abelian extension theory of Rota—Baxter algebras of weight zero, and classify them by introducing the non-abelian cohomology. Next, given a non-abelian extension $0\rightarrow B_S\rightarrow E_U\rightarrow A_R\rightarrow 0$ of Rota—Baxter algebras, we construct the Wells type exact sequences, and find their role in extending a Rota—Baxter automorphism $\beta\in\operatorname{Aut}(B_S)$ and lifting a Rota—Baxter automorphism $\alpha\in\operatorname{Aut}(A_R)$ to an automorphism in $\operatorname{Aut}(E_U)$. We end this paper by considering a similar study for dendriform algebras.