Construction of Rota-Baxter algebras via Hopf module algebras

Abstract

We propose the notion of Hopf module algebras and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight -1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application, we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.

8 pages, some typos are corrected and some statements are improved; accepted for publication in Sci China Math