| Title:
|
Yetter-Drinfeld-Long bimodules are modules (English) |
| Author:
|
Lu, Daowei |
| Author:
|
Wang, Shuanhong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
379-387 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hopf algebra |
| Keyword:
|
Yetter-Drinfeld-Long bimodule |
| Keyword:
|
braided monoidal category |
| MSC:
|
16T05 |
| MSC:
|
18D10 |
| idZBL:
|
Zbl 06738525 |
| idMR:
|
MR3661047 |
| DOI:
|
10.21136/CMJ.2017.0666-15 |
| . |
| Date available:
|
2017-06-01T14:27:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146762 |
| . |
| Reference:
|
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| Reference:
|
[2] Panaite, F., Staic, M. D.: More examples of pseudosymmetric braided categories.J. Algebra Appl. 12 (2013), Paper No. 1250186, 21 pages. Zbl 1275.18018, MR 3037261, 10.1142/S0219498812501861 |
| Reference:
|
[3] Panaite, F., Staic, M. D., Oystaeyen, F. Van: Pseudosymmetric braidings, twines and twisted algebras.J. Pure Appl. Algebra 214 (2010), 867-884. Zbl 1207.16037, MR 2580665, 10.1016/j.jpaa.2009.08.008 |
| Reference:
|
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| Reference:
|
[5] Panaite, F., Oystaeyen, F. Van: L-R-smash biproducts, double biproducts and a braided category of Yetter-Drinfeld-Long bimodules.Rocky Mt. J. Math. 40 (2010), 2013-2024. Zbl 1206.16021, MR 2764235, 10.1216/RMJ-2010-40-6-2013 |
| Reference:
|
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| Reference:
|
[7] Zhang, L.: L-R smash products for bimodule algebras.Prog. Nat. Sci. 16 (2006), 580-587. Zbl 1124.16036, MR 2247240, 10.1080/10020070612330038 |
| . |
