On the Wakamatsu tilting conjecture
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918103730880512 |
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| author | Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud |
| author_facet | Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud |
| contents | Let R be an associative ring with identity. We establish that the generalized Auslander-Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting R-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for R in two cases: when R is a left Artinian local ring or when it is the group ring of a finite group G over a commutative Artinian ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Wakamatsu tilting conjecture Divaani-Aazar, Kamran Fallah, Ali Mahin Tousi, Massoud Representation Theory 16D20, 16G99, 18G05, 18E40 Let R be an associative ring with identity. We establish that the generalized Auslander-Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting R-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for R in two cases: when R is a left Artinian local ring or when it is the group ring of a finite group G over a commutative Artinian ring. |
| title | On the Wakamatsu tilting conjecture |
| topic | Representation Theory 16D20, 16G99, 18G05, 18E40 |
| url | https://arxiv.org/abs/2407.06353 |