Rota-Bater paried comodule and Rota-Bater paired Hopf module

TL;DR

This paper introduces Rota-Baxter paired comodules, explores their properties, and constructs them on various algebraic structures, culminating in the definition and structure theorem of Rota-Baxter paired Hopf modules.

Contribution

It defines Rota-Baxter paired comodules, characterizes them, and constructs Rota-Baxter paired Hopf modules, extending the theory of Rota-Baxter structures in algebra.

Findings

Characterization of generic Rota-Baxter paired comodules

Construction of Rota-Baxter paired comodules on Hopf-related structures

Structure theorem for generic Rota-Baxter paired Hopf modules

Abstract

In this paper, we introduce the conception of Rota-Baxter paired comodules, which is dual to Rota-Baxter paired modules in [14]. We mainly discuss some properties of Rota-Baxter paired comodules, especially we give the characterization of generic Rota-Baxter paired comodules, which has 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. And then we finally introduce the conception of Rota-Baxter paired Hopf modules by combining Rota-Baxter paired module with Rota-Baxter paired comodule, and give the structure theorem of generic Rota-Baxter paired Hopf modules.