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Yetter-Drinfeld-Long bimodules are modules
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 379-387 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $H$ be a finite-dimensional bialgebra. In this paper, we prove that the category $\mathcal {LR}(H)$ of Yetter-Drinfeld-Long bimodules, introduced by F. Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category $^{H\otimes H^*}_{H\otimes H^*}\mathcal {YD}$ over the tensor product bialgebra $H\otimes H^*$ as monoidal categories. Moreover if $H$ is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results.
Let $H$ be a finite-dimensional bialgebra. In this paper, we prove that the category $\mathcal {LR}(H)$ of Yetter-Drinfeld-Long bimodules, introduced by F. Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category $^{H\otimes H^*}_{H\otimes H^*}\mathcal {YD}$ over the tensor product bialgebra $H\otimes H^*$ as monoidal categories. Moreover if $H$ is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results.
DOI : 10.21136/CMJ.2017.0666-15
Classification : 16T05, 18D10
Keywords: Hopf algebra; Yetter-Drinfeld-Long bimodule; braided monoidal category 
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Lu, Daowei; Wang, Shuanhong. Yetter-Drinfeld-Long bimodules are modules. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 379-387. doi: 10.21136/CMJ.2017.0666-15

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