Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916777821208576 |
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| author | McHugh, John Revere |
| author_facet | McHugh, John Revere |
| contents | We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation equivalent. These results help to clarify the distinction between a $p$-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a $p$-permutation equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent McHugh, John Revere Representation Theory Group Theory We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation equivalent. These results help to clarify the distinction between a $p$-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a $p$-permutation equivalence. |
| title | Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent |
| topic | Representation Theory Group Theory |
| url | https://arxiv.org/abs/2506.03446 |