English

Rota-Baxter paired modules and their constructions from Hopf algebras

Quantum Algebra 2020-07-27 v1

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}
}