Four-angle Hopf modules for Hom-Hopf algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866908944463560704 |
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| author | Liu, Xiaoqian Yan, Dongdong Deng, Xuchen Wang, Danhua |
| author_facet | Liu, Xiaoqian Yan, Dongdong Deng, Xuchen Wang, Danhua |
| contents | In this paper, we introduce the notion of a four-angle Hopf module for a Hom-Hopf algebra $(H,β)$ and show that the category $\!^{H}_{H}\mathfrak{M}^{H}_{H}$
of four-angle Hopf modules is a monoidal category with either a Hom-tensor product $\otimes_{H}$ or a Hom-cotensor product $\Box_{H}$ as a monoidal product.
We study the category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules with bijective structure map can be organized as a braided monoidal category, in which we use a new monoidal structure. Finally, We prove an equivalence between the monoidal category $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ or $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$ of four-angle Hopf modules, and the monoidal category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules,
and furthermore, we give a braiding structure of the monoidal categorys $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ (and $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_15267 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Four-angle Hopf modules for Hom-Hopf algebras Liu, Xiaoqian Yan, Dongdong Deng, Xuchen Wang, Danhua Rings and Algebras Representation Theory 16D20, 16D90, 18M15 In this paper, we introduce the notion of a four-angle Hopf module for a Hom-Hopf algebra $(H,β)$ and show that the category $\!^{H}_{H}\mathfrak{M}^{H}_{H}$ of four-angle Hopf modules is a monoidal category with either a Hom-tensor product $\otimes_{H}$ or a Hom-cotensor product $\Box_{H}$ as a monoidal product. We study the category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules with bijective structure map can be organized as a braided monoidal category, in which we use a new monoidal structure. Finally, We prove an equivalence between the monoidal category $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ or $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$ of four-angle Hopf modules, and the monoidal category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules, and furthermore, we give a braiding structure of the monoidal categorys $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ (and $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$). |
| title | Four-angle Hopf modules for Hom-Hopf algebras |
| topic | Rings and Algebras Representation Theory 16D20, 16D90, 18M15 |
| url | https://arxiv.org/abs/2006.15267 |