Article
| Title: | Classification of irreducible representations of near-group fusion algebras (English) |
| Author: | Li, Xiaoming |
| Author: | Zhang, Xinru |
| Author: | Li, Libin |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 821-837 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We explicitly classify the irreducible representations of the near-group fusion algebra associated with a finite group over a field with arbitrary characteristic. (English) |
| Keyword: | simple module |
| Keyword: | near-group fusion ring |
| MSC: | 16D60 |
| MSC: | 16G10 |
| DOI: | 10.21136/CMJ.2025.0420-24 |
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| Date available: | 2025-09-19T11:49:29Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153054 |
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| Reference: | [6] Izumi, M.: A Cuntz algebra approach to the classification of near-group categories.Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F. R. Jones' 60th Birthday Australian National University, Canberra (2017), 222-343. Zbl 1403.46049, MR 3635673 |
| Reference: | [7] Ostrik, V.: On formal codegrees of fusion categories.Math. Res. Lett. 16 (2009), 895-901. Zbl 1204.18003, MR 2576705, 10.4310/MRL.2009.v16.n5.a11 |
| Reference: | [8] Ostrik, V.: Pivotal fusion categories of rank 3.Mosc. Math. J. 15 (2015), 373-396. Zbl 1354.18009, MR 3427429, 10.17323/1609-4514-2015-15-2-373-396 |
| Reference: | [9] Seitz, G.: Finite groups having only one irreducible representation of degree greater than one.Proc. Am. Math. Soc. 19 (1968), 459-461. Zbl 0244.20010, MR 0222160, 10.1090/S0002-9939-1968-0222160-X |
| Reference: | [10] Tambara, D., Yamagami, S.: Tensor categories with fusion rules of self-duality for finite abelian groups.J. Algebra 209 (1998), 692-707. Zbl 0923.46052, MR 1659954, 10.1006/jabr.1998.7558 |
| Reference: | [11] Wang, Z., Liu, G., Li, L.: The Casimir number and the determinant of a fusion category.Glasg. Math. J. 63 (2021), 438-450. Zbl 1469.18025, MR 4244208, 10.1017/S0017089520000294 |
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