Permutation dimensions of prime cyclic groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914104230281216 |
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| author | Walsh, Jack |
| author_facet | Walsh, Jack |
| contents | Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by replacing projective resolutions of ring modules with resolutions by p-permutation modules of modules over the group ring. We compute this invariant for cyclic groups of prime order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutation dimensions of prime cyclic groups Walsh, Jack Representation Theory Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by replacing projective resolutions of ring modules with resolutions by p-permutation modules of modules over the group ring. We compute this invariant for cyclic groups of prime order. |
| title | Permutation dimensions of prime cyclic groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2504.11841 |