A characterization of 2-fold torsion classes induced by $τ$-rigid modules
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909537212039168 |
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| author | Uchida, Yuki |
| author_facet | Uchida, Yuki |
| contents | We introduce $n$-fold torsion(-free) classes of an abelian category. These are a generalization of ordinary torsion(-free) classes in the sense that $1$-fold torsion(-free) classes coincide with torsion(-free) classes. In the category of finitely generated modules over a finite dimensional algebra, we can naturally construct $n$-fold torsion classes from $τ$-rigid modules. We characterize the $2$-fold torsion classes induced by $τ$-rigid modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of 2-fold torsion classes induced by $τ$-rigid modules Uchida, Yuki Representation Theory Rings and Algebras We introduce $n$-fold torsion(-free) classes of an abelian category. These are a generalization of ordinary torsion(-free) classes in the sense that $1$-fold torsion(-free) classes coincide with torsion(-free) classes. In the category of finitely generated modules over a finite dimensional algebra, we can naturally construct $n$-fold torsion classes from $τ$-rigid modules. We characterize the $2$-fold torsion classes induced by $τ$-rigid modules. |
| title | A characterization of 2-fold torsion classes induced by $τ$-rigid modules |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2503.11184 |