Total stability and Auslander-Reiten theory for Dynkin quivers

Fuente: arXiv
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Autores principales: Diaz, Yariana, Gilbert, Cody, Kinser, Ryan
Formato: Preprint
Publicado: 2022
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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