2025/03/11 by Daowei Lu, Lu, Daowei, D. F. Wang +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2503.08021
openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A and H be two cocommutative Hopf algebras such that A is an H-bimodule Hopf algebra. Suppose that R:A→ A is a linear map and B is a Rota-Baxter operator of H. In this paper we will characterize the Rota-Baxter operators on the L-R smash product A\natural H and give the necessary and sufficient conditions to make B a Rota-Baxter operator of A\natural H. Then we will consider the dual case, and construct a Rota-Baxter co-operator on the L-R smash coproduct C\ltimes H, where C and H are commutative Hopf algebras and C is an H-bicomodule Hopf algebra.