Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 379-387, 2017

Yetter-Drinfeld-Long bimodules are modules

Daowei Lu, Shuanhong Wang

Received December 9, 2015.  First published March 3, 2017.

Abstract:  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.
Keywords:  Hopf algebra; Yetter-Drinfeld-Long bimodule; braided monoidal category
Classification MSC:  16T05, 18D10
DOI:  10.21136/CMJ.2017.0666-15

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Affiliations:   Daowei Lu (corresponding author), Department of Mathematics, Jining University, No. 1 Xingtan Road, Qufu 273155, Shandong, P. R. of China, e-mail:; Shuanhong Wang, School of Mathematics, Southeast University, No. 2 Sipailou, Nanjing 210096, Jiangsu, P. R. of China, e-mail:

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