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

2022/06/17 by Das, Apurba, Rathee, Nishant
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/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 → B_S → E_U → A_R → 0 of Rota-Baxter algebras, we construct the Wells type exact sequences and find their role in extending a Rota-Baxter automorphism β∈ Aut(B_S) and lifting a Rota-Baxter automorphism α∈ Aut(A_R) to an automorphism in Aut(E_U). We end this paper by considering a similar study for dendriform algebras.

Related

• Non-abelian extensions of relative Rota-Baxter Lie algebras and Wells type exact sequences
• Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms
• Bimodules over relative Rota-Baxter algebras and cohomologies
• Rota-Baxter systems, dendriform algebras and covariant bialgebras
• Deformations and Cohomology Theory of Rota-Baxter Systems