On Morita equivalences with endopermutation source and isotypies
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915171878830080 |
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| author | Huang, Xin |
| author_facet | Huang, Xin |
| contents | We introduce a new type of equivalence between blocks of finite group algebras called an almost isotypy. An almost isotypy restricts to a weak isotypy in Broué's original definition, and it is slightly weaker than Linckelmann's version. We show that a bimodule of two block algebras of finite groups - which has an endopermutation module as a source and which induces a Morita equivalence - gives rise, via slash functors, to an almost isotypy if the character values of a (hence any) source are rational integers. Consequently, if two blocks are Morita equivalent via a bimodule with endopermutation source, then they are almost isotypic. We also explain why the notion of almost isotypies is reasonable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Morita equivalences with endopermutation source and isotypies Huang, Xin Representation Theory Group Theory 20C20 We introduce a new type of equivalence between blocks of finite group algebras called an almost isotypy. An almost isotypy restricts to a weak isotypy in Broué's original definition, and it is slightly weaker than Linckelmann's version. We show that a bimodule of two block algebras of finite groups - which has an endopermutation module as a source and which induces a Morita equivalence - gives rise, via slash functors, to an almost isotypy if the character values of a (hence any) source are rational integers. Consequently, if two blocks are Morita equivalent via a bimodule with endopermutation source, then they are almost isotypic. We also explain why the notion of almost isotypies is reasonable. |
| title | On Morita equivalences with endopermutation source and isotypies |
| topic | Representation Theory Group Theory 20C20 |
| url | https://arxiv.org/abs/2405.20268 |