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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2312.15586 |
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| _version_ | 1866916076050186240 |
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| author | Liu, Hui Zhang, Xiaojin Zhang, Yingying |
| author_facet | Liu, Hui Zhang, Xiaojin Zhang, Yingying |
| contents | We first introduce the notion of $CM$-$τ$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$τ$-tilting free algebras. Then we give a bijection between Gorenstein projective $τ$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $τ$-rigid modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15586 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Applications of Gorenstein projective $τ$-rigid modules Liu, Hui Zhang, Xiaojin Zhang, Yingying Representation Theory Rings and Algebras 16G10 We first introduce the notion of $CM$-$τ$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$τ$-tilting free algebras. Then we give a bijection between Gorenstein projective $τ$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $τ$-rigid modules. |
| title | Applications of Gorenstein projective $τ$-rigid modules |
| topic | Representation Theory Rings and Algebras 16G10 |
| url | https://arxiv.org/abs/2312.15586 |