Article
| Title: | Remarks on Sekine quantum groups (English) |
| Author: | Chen, Jialei |
| Author: | Yang, Shilin |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 695-707 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We first describe the Sekine quantum groups $\mathcal {A}_{k}$ (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of $\mathcal {A}_{k}$ and describe their representation rings $r(\mathcal {A}_{k})$. Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of $r(\mathcal {A}_{k})$. (English) |
| Keyword: | Sekine quantum group |
| Keyword: | representation ring |
| Keyword: | Casimir number |
| MSC: | 16D70 |
| MSC: | 16G10 |
| MSC: | 16T05 |
| idZBL: | Zbl 07584096 |
| idMR: | MR4467936 |
| DOI: | 10.21136/CMJ.2022.0112-21 |
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| Date available: | 2022-08-22T08:17:57Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150611 |
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| Reference: | [6] Vaes, S., Vainerman, L.: Extensions of locally compact quantum groups and the bicrossed product construction.Adv. Math. 175 (2003), 1-101. Zbl 1034.46068, MR 1970242, 10.1016/S0001-8708(02)00040-3 |
| Reference: | [7] Wang, Z., Li, L., Zhang, Y.: A criterion for the Jacobson semisimplicity of the Green ring of a finite tensor category.Glasg. Math. J. 60 (2018), 253-272. Zbl 1444.16025, MR 3733845, 10.1017/S0017089517000246 |
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