Total stability and Auslander-Reiten theory for Dynkin quivers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917721760858112 |
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| author | Diaz, Yariana Gilbert, Cody Kinser, Ryan |
| author_facet | Diaz, Yariana Gilbert, Cody Kinser, Ryan |
| contents | This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability function to be totally stable (i.e. to make every indecomposable stable). Namely, a stability function $μ$ is totally stable if and only if $μ(τV) < μ(V)$ for every almost split sequence $0 \to τV \to E \to V \to 0$ where $E$ is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02445 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Total stability and Auslander-Reiten theory for Dynkin quivers Diaz, Yariana Gilbert, Cody Kinser, Ryan Representation Theory This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability function to be totally stable (i.e. to make every indecomposable stable). Namely, a stability function $μ$ is totally stable if and only if $μ(τV) < μ(V)$ for every almost split sequence $0 \to τV \to E \to V \to 0$ where $E$ is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver. |
| title | Total stability and Auslander-Reiten theory for Dynkin quivers |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2208.02445 |