| Autor: |
Wenxia Wu, Yunnan Li |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 9, Iss 7, Pp 19859-19887 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2024970?viewType=HTML |
| Popis: |
The complex representation rings of finite groups are the fundamental class of fusion rings, categorified by the corresponding fusion categories of complex representations. The category of $ \mathbb{Z}_+ $-modules of finite rank over such a representation ring is also semisimple. In this paper, we classify the irreducible based modules of rank up to 5 over the complex representation ring $ r(S_4) $ of the symmetric group $ S_4 $. In total, 16 inequivalent irreducible based modules were obtained. In this process, the MATLAB program was used in order to obtain some representation matrices. Based on such a classification result, we further discuss the categorification of based modules over $ r(S_4) $ by module categories over the complex representation category $ {\rm Rep}(S_4) $ of $ S_4 $ arisen from projective representations of certain subgroups of $ S_4 $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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