Hopf heap modules, Rota-Baxter operators, and their structure theorems

Abstract

This paper is primarily devoted to the study of Hopf heaps and Hopf heap modules. We redefine the structure of Hopf trusses by means of Hopf heaps, establish the connection between Hopf trusses and Hopf braces, and provide a series of examples of Hopf truss structures from the perspective of Hopf heaps. Most importantly, we introduce the conception of Hopf heap modules, and present its structure theorem. Finally, we introduce the notions of Rota-Baxter operators on Hopf heaps and Hopf heap modules, and present the structure theorem for Rota-Baxter Hopf heap modules.