A characterization of IE-closed subcategories via canonical twin support $τ$-tilting modules
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917380803788800 |
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| author | Gao, Hanpeng Liu, Dajun Liu, Yu-Zhe |
| author_facet | Gao, Hanpeng Liu, Dajun Liu, Yu-Zhe |
| contents | Enomoto and Sakai classified IE-closed subcategories over hereditary algebras via twin rigid modules. However, this classification inherently relies on the vanishing of second extension spaces, thus failing for arbitrary finite-dimensional algebras. In this paper, we generalize their classification to arbitrary finite-dimensional algebras by introducing the notions of canonical twin support $τ$-tilting modules and canonical Ext-pairs. By utilizing functorially finite torsion pairs, we provide a homological characterization of these modules. Furthermore, we establish explicit bijections up to isomorphism among functorially finite IE-closed subcategories, canonical twin support $τ$-tilting modules, and canonical Ext-pairs. Finally, we provide a constructive algorithm to canonicalize any given twin support $τ$-tilting module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A characterization of IE-closed subcategories via canonical twin support $τ$-tilting modules Gao, Hanpeng Liu, Dajun Liu, Yu-Zhe Representation Theory 16G10, 16G30 Enomoto and Sakai classified IE-closed subcategories over hereditary algebras via twin rigid modules. However, this classification inherently relies on the vanishing of second extension spaces, thus failing for arbitrary finite-dimensional algebras. In this paper, we generalize their classification to arbitrary finite-dimensional algebras by introducing the notions of canonical twin support $τ$-tilting modules and canonical Ext-pairs. By utilizing functorially finite torsion pairs, we provide a homological characterization of these modules. Furthermore, we establish explicit bijections up to isomorphism among functorially finite IE-closed subcategories, canonical twin support $τ$-tilting modules, and canonical Ext-pairs. Finally, we provide a constructive algorithm to canonicalize any given twin support $τ$-tilting module. |
| title | A characterization of IE-closed subcategories via canonical twin support $τ$-tilting modules |
| topic | Representation Theory 16G10, 16G30 |
| url | https://arxiv.org/abs/2603.13006 |