Article
| Title: | Special modules for $R({\rm PSL}(2,q))$ (English) |
| Author: | Cao, Liufeng |
| Author: | Chen, Huixiang |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1301-1317 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a fusion ring and $R_\mathbb {C}:=R\otimes _\mathbb {Z}\mathbb {C}$ be the corresponding fusion algebra. We first show that the algebra $R_\mathbb {C}$ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, $R_\mathbb {C}$ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra $R({\rm PSL}(2,q)):=r({\rm PSL}(2,q))\otimes _\mathbb {Z}\mathbb {C}$ up to isomorphism, where $r({\rm PSL}(2,q))$ is the interpolated fusion ring with even $q\geq 2$. (English) |
| Keyword: | Frobenius-Perron theorem |
| Keyword: | special module |
| Keyword: | fusion ring |
| MSC: | 16G99 |
| DOI: | 10.21136/CMJ.2023.0002-23 |
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| Date available: | 2023-11-23T12:29:23Z |
| Last updated: | 2023-11-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151961 |
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