Intersection vectors over skew-tilings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911268376412160 |
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| author | Deng, Difan Geng, Shengfei Liu, Pin |
| author_facet | Deng, Difan Geng, Shengfei Liu, Pin |
| contents | We prove that under a mild condition, a multiset of tagged permissible arcs over a skew-tiling is uniquely determined by its intersection vector. As an application, it is proved that -- up to isomorphism -- different $τ$-rigid modules over a skew-gentle algebra $A$ arising from a skew-triple $(Q,Sp,I)$ have different dimension vectors if and only if $(Q,I)$ has no minimal oriented cycle of even-length with full zero relations. This generalizes a recent work of Fu-Geng for gentle algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection vectors over skew-tilings Deng, Difan Geng, Shengfei Liu, Pin Representation Theory We prove that under a mild condition, a multiset of tagged permissible arcs over a skew-tiling is uniquely determined by its intersection vector. As an application, it is proved that -- up to isomorphism -- different $τ$-rigid modules over a skew-gentle algebra $A$ arising from a skew-triple $(Q,Sp,I)$ have different dimension vectors if and only if $(Q,I)$ has no minimal oriented cycle of even-length with full zero relations. This generalizes a recent work of Fu-Geng for gentle algebras. |
| title | Intersection vectors over skew-tilings |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2511.12619 |