Matrix units in the simple components of rational group algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909224090468352 |
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| author | Bakshi, Gurmeet Kaur Garg, Jyoti |
| author_facet | Bakshi, Gurmeet Kaur Garg, Jyoti |
| contents | For the rational group algebra $\mathbb{Q}G$ of a finite group $G$, we provide an effective method to compute a complete set of matrix units and, in particular, primitive orthogonal idempotents in a simple component of $\mathbb{Q}G$, which is realized by a generalized strongly monomial character and has a prime Schur index. We also provide some classes of groups $G$ where this method can be successfully applied. The application of the method developed is also illustrated with detailed computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix units in the simple components of rational group algebras Bakshi, Gurmeet Kaur Garg, Jyoti Rings and Algebras Representation Theory 17C27, 20C05, 16K20, 16S35, 16U40 For the rational group algebra $\mathbb{Q}G$ of a finite group $G$, we provide an effective method to compute a complete set of matrix units and, in particular, primitive orthogonal idempotents in a simple component of $\mathbb{Q}G$, which is realized by a generalized strongly monomial character and has a prime Schur index. We also provide some classes of groups $G$ where this method can be successfully applied. The application of the method developed is also illustrated with detailed computations. |
| title | Matrix units in the simple components of rational group algebras |
| topic | Rings and Algebras Representation Theory 17C27, 20C05, 16K20, 16S35, 16U40 |
| url | https://arxiv.org/abs/2406.10113 |