Matched pairs of Hopf algebras and Rota-Baxter Hopf algebras

2025/11/29 by Wang, Shukun
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.00286

Abstract

In this paper, we first study Rota-Baxter Hopf algebras of weight -1 and construct a matched pair of Hopf algebras on every Rota-Baxter Hopf algebra of weight -1. Then we propose the notion of projection homomorphism pairs on a matched pair of Hopf algebras, and show that every projection homomorphism pair (C,\wtdC) induces a Rota-Baxter Hopf algebra. Conversely, we prove that the matched pair of Hopf algebras on a Rota-Baxter Hopf algebra of weight -1 (H,B) gives rise to a projection homomorphism pair (C,\wtdC). Furthermore, we study the Rota-Baxter Hopf algebra structure on \im C that is Rota-Baxter isomorphic to (H,B), and investigate the relationship between the Rota-Baxter Hopf algebra structure on \im \wtdC and the descendent Rota-Baxter Hopf algebra (H_B,B).

Citations

• Matched pairs and Yang-Baxter operators
• Yetter-Drinfeld post-Hopf algebras and Yetter-Drinfeld relative Rota-Baxter operators
• Matched pairs and Yetter-Drinfeld braces
• Rota-Baxter operators on cocommutative Hopf algebras and Hopf braces
• Factorizable Lie Bialgebras, Quadratic Rota–Baxter Lie Algebras and Rota–Baxter Lie Bialgebras
• Rota-Baxter operators on cocommutative Hopf algebras
• Integrable Systems and Factorization Problems
• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem

Related

• Rota-Baxter co-operators on commutative Hopf algebras
• Rota-Baxter systems of Hopf algebras and Hopf trusses
• Rota-Baxter operators on cocommutative Hopf algebras and Hopf braces
• Rota-Bater paried comodule and Rota-Bater paired Hopf module
• Constructions of Rota-Baxter operators by L-R smash products