Rota-Baxter paired modules and their constructions from Hopf algebras
Abstract
In this paper, we introduce the concept of a Rota-Baxter paired module to study Rota-Baxter modules without necessarily a Rota-Baxter operator. We obtain two characterizations of Rota-Baxter paired modules, and give some basic properties of Rota-Baxter paired modules. Beginning with the connection between the notion of integrals in the representations of Hopf algebra and of the notion of an integral algebra as a motivation and special case of Rota-Baxter algebra of weight zero, we obtain a large number of Rota-Baxter paired modules from Hopf related algebras and modules, including semisimple Hopf algebras, weak Hopf algebras, Long bialgebras, quasitriangular Hopf algebras, weak Hopf modules, dimodules and Doi-Hopf modules. Some of them give new examples of Rota-Baxter algebras.
Keywords
Cite
@article{arxiv.1710.03880,
title = {Rota-Baxter paired modules and their constructions from Hopf algebras},
author = {Huihui Zheng and Li Guo and Liangyun Zhang},
journal= {arXiv preprint arXiv:1710.03880},
year = {2020}
}