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arXiv · 2208.02445

Total stability and Auslander-Reiten theory for Dynkin quivers

Yariana Diaz·Cody Gilbert·Ryan Kinser
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Abstract

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 $\mu$ is totally stable if and only if $\mu(\tau V) < \mu(V)$ for every almost split sequence $0 \to \tau V \to E \to V \to 0$ where $E$ is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver.

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BibTeXRIS

Yariana Diaz, Cody Gilbert, Ryan Kinser. 2022-08-04. Total stability and Auslander-Reiten theory for Dynkin quivers. https://arxiv.org/abs/2208.02445

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