Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 379–387

Yetter-Drinfeld-Long bimodules are modules

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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 HH* 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 

MSC 2010

16T05 18D10 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsJining UniversityQufu, ShandongP.R. of China
  2. 2.School of MathematicsSoutheast UniversityNanjing, JiangsuP.R. of China

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