Article
| Title: | The Grothendieck ring of quantum double of quaternion group (English) |
| Author: | Sun, Hua |
| Author: | Pang, Jia |
| Author: | Shen, Yanxi |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 881-896 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\Bbbk $ be an algebraically closed field of characteristic $p\neq 2$, and let $Q_8$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D(\Bbbk Q_8)$ of group algebra $\Bbbk Q_8$. Moreover, we investigate the tensor product decomposition rules of all simple $D(\Bbbk Q_8)$-modules. Finally, we describe the Grothendieck ring $G_0(D(\Bbbk Q_8))$ by generators with relations. (English) |
| Keyword: | Grothendieck ring |
| Keyword: | simple module |
| Keyword: | quantum double |
| Keyword: | quaternion group |
| MSC: | 16G30 |
| MSC: | 16T99 |
| DOI: | 10.21136/CMJ.2024.0113-24 |
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| Date available: | 2024-10-03T12:39:15Z |
| Last updated: | 2024-10-04 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152586 |
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