| Title:
|
Braided coproduct, antipode and adjoint action for $U_q(sl_2)$ (English) |
| Author:
|
Pandžić, Pavle |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
5 |
| Year:
|
2024 |
| Pages:
|
365-376 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Motivated by our attempts to construct an analogue of the Dirac operator in the setting of $U_q(\mathfrak{sl}_n)$, we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra $U_q(\mathfrak{sl}_2)$. The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid. (English) |
| Keyword:
|
quantum group |
| Keyword:
|
quantum $\mathfrak{sl}_2$ |
| Keyword:
|
quantum adjoint action |
| Keyword:
|
tensor categories |
| Keyword:
|
braided tensor product |
| Keyword:
|
braided adjoint action |
| MSC:
|
16T20 |
| MSC:
|
20G42 |
| idZBL:
|
Zbl 07980758 |
| idMR:
|
MR4840183 |
| DOI:
|
10.5817/AM2024-5-365 |
| . |
| Date available:
|
2024-12-13T18:51:00Z |
| Last updated:
|
2025-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152657 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[10] Pandžić, P., Somberg, P.: Dirac operator for the quantum group $U_q(\mathfrak{sl}_3)$.in preparation. |
| Reference:
|
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| Reference:
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| Reference:
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| . |
