Abstract
Let H be a finite-dimensional bialgebra. In this paper, we prove that the category ℒR(H) of Yetter-Drinfeld-Long bimodules, introduced by F. Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category \({}_{H \otimes H*}^{H \otimes H*}YD\) over the tensor product bialgebra H ⊗ 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.
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This work was supported by the NSF of China (No. 11371088) and the Fundamental Research Funds for the Central Universities (No. KYLX15 0109).
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Lu, D., Wang, S. Yetter-Drinfeld-Long bimodules are modules. Czech Math J 67, 379–387 (2017). https://doi.org/10.21136/CMJ.2017.0666-15
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DOI: https://doi.org/10.21136/CMJ.2017.0666-15