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arXiv · 1710.03880

Rota-Baxter paired modules and their constructions from Hopf algebras

Huihui Zheng·Li Guo·Liangyun Zhang
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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.

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Huihui Zheng, Li Guo, Liangyun Zhang. 2017-10-11. Rota-Baxter paired modules and their constructions from Hopf algebras. https://arxiv.org/abs/1710.03880

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