A unified extension theory of Rota-Baxter algebras, dendriform algebras, and a fundamental sequence of Wells

Apurba Das; Nishant Rathee

paper

A unified extension theory of Rota-Baxter algebras, dendriform algebras, and a fundamental sequence of Wells

arXiv:2206.09019

Abstract

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 and classify them by introducing the non-abelian cohomology. Next, given a non-abelian extension $0 \to B_{S} \to E_{U} \to A_{R} \to 0$ of Rota-Baxter algebras, we construct the Wells type exact sequences and find their role in extending a Rota-Baxter automorphism $β \in Aut (B_{S})$ and lifting a Rota-Baxter automorphism $α \in Aut (A_{R})$ to an automorphism in $Aut (E_{U})$ . We end this paper by considering a similar study for dendriform algebras.

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