When are permutation invariants Cohen-Macaulay?
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910059627282432 |
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| author | Campbell, H. E. A. Wehlau, David L. |
| author_facet | Campbell, H. E. A. Wehlau, David L. |
| contents | Over a field of characteristic 0, every ring of invariants of a finite group is Cohen-Macaulay. This is not true for fields of positive characteristic. We consider permutation representations and their invariant rings over fields $\mathbb{F}_p$ of prime order. We give an efficient algorithm which for any given permutation representation, determines those primes $p$ for which the invariant ring over $\mathbb{F}_p$ is Cohen-Macaulay, using linear algebra over $\ZZ$. A generalization of the classical discriminant associated to the alternating group is defined for subgroups of certain finite unitary complex reflection groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09056 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | When are permutation invariants Cohen-Macaulay? Campbell, H. E. A. Wehlau, David L. Commutative Algebra 13A50 (Primary) 20F55, 14M05 (Secondary) Over a field of characteristic 0, every ring of invariants of a finite group is Cohen-Macaulay. This is not true for fields of positive characteristic. We consider permutation representations and their invariant rings over fields $\mathbb{F}_p$ of prime order. We give an efficient algorithm which for any given permutation representation, determines those primes $p$ for which the invariant ring over $\mathbb{F}_p$ is Cohen-Macaulay, using linear algebra over $\ZZ$. A generalization of the classical discriminant associated to the alternating group is defined for subgroups of certain finite unitary complex reflection groups. |
| title | When are permutation invariants Cohen-Macaulay? |
| topic | Commutative Algebra 13A50 (Primary) 20F55, 14M05 (Secondary) |
| url | https://arxiv.org/abs/2308.09056 |