Yetter-Drinfeld-Long bimodules are modules
Czechoslovak Mathematical Journal (2017)
- Volume: 67, Issue: 2, page 379-387
- ISSN: 0011-4642
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topLu, Daowei, and Wang, Shuan Hong. "Yetter-Drinfeld-Long bimodules are modules." Czechoslovak Mathematical Journal 67.2 (2017): 379-387. <http://eudml.org/doc/288181>.
@article{Lu2017,
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.},
author = {Lu, Daowei, Wang, Shuan Hong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hopf algebra; Yetter-Drinfeld-Long bimodule; braided monoidal category},
language = {eng},
number = {2},
pages = {379-387},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Yetter-Drinfeld-Long bimodules are modules},
url = {http://eudml.org/doc/288181},
volume = {67},
year = {2017},
}
TY - JOUR
AU - Lu, Daowei
AU - Wang, Shuan Hong
TI - Yetter-Drinfeld-Long bimodules are modules
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 379
EP - 387
AB - 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.
LA - eng
KW - Hopf algebra; Yetter-Drinfeld-Long bimodule; braided monoidal category
UR - http://eudml.org/doc/288181
ER -
References
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