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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.02445 |
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Table of 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.