Yetter-Drinfeld-Long bimodules are modules

Czechoslovak Mathematical Journal

Daowei Lu, Shuanhong Wang¹ 

关键词: Hopf algebra;    Yetter-Drinfeld-Long bimodule;    braided monoidal category;   

DOI  :  10.21136/CMJ.2017.0666-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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.

【 授权许可】

Unknown