Article
| Title: | $C^*$-basic construction between non-balanced quantum doubles (English) |
| Author: | Xin, Qiaoling |
| Author: | Cao, Tianqing |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 611-621 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | For finite groups $X$, $G$ and the right $G$-action on $X$ by group automorphisms, the non-balanced quantum double $D(X;G)$ is defined as the crossed product $(\Bbb {C}X^{\rm op})^*\rtimes \Bbb {C}G$. We firstly prove that $D(X;G)$ is a finite-dimensional Hopf $C^*$-algebra. For any subgroup $H$ of $G$, $D(X;H)$ can be defined as a Hopf $C^*$-subalgebra of $D(X;G)$ in the natural way. Then there is a conditonal expectation from $D(X;G)$ onto $D(X;H)$ and the index is $[G;H]$. Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra. (English) |
| Keyword: | non-balanced quantum double |
| Keyword: | $C^*$-basic construction |
| Keyword: | crossed product |
| Keyword: | action |
| MSC: | 16S35 |
| MSC: | 46L05 |
| DOI: | 10.21136/CMJ.2024.0022-24 |
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| Date available: | 2024-07-10T14:58:40Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152461 |
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