Rota–Baxter paired comodules and Rota–Baxter paired Hopf modules

Abstract

We introduce the concept of Rota-Baxter paired comodules, which is dual to Rota-Baxter paired modules defined by Zheng et al. (2020). We discuss some properties of Rota-Baxter paired comodules, in particular we give a characterization of generic Rota-Baxter paired comodules, which has an important application for the construction of Rota-Baxter comodules. Moreover, we construct Rota-Baxter paired comodules on Hopf algebras, weak Hopf algebras, weak Hopf modules, dimodules, relative Hopf modules and Rota-Baxter paired comodules. We also introduce the concept of Rota-Baxter paired Hopf modules by combining the notion of Rota-Baxter paired module with Rota-Baxter paired comodule, and prove a structure theorem for generic Rota-Baxter paired Hopf modules.