Total stability and Auslander-Reiten theory for Dynkin quivers

Yariana Diaz; Cody Gilbert; Ryan Kinser

doi:10.48550/arXiv.2208.02445

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Total stability and Auslander-Reiten theory for Dynkin quivers

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Total stability and Auslander-Reiten theory for Dynkin quivers

Yariana Diaz, Cody Gilbert and Ryan Kinser

ArXiv.org

08/04/2022

DOI: 10.48550/arXiv.2208.02445

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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 μ is totally stable if and only if μ(τV)<μ(V) for every almost split sequences 0→τV→E→V→0 where E is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver.

Mathematics - Representation Theory

Details

Title: Subtitle: Total stability and Auslander-Reiten theory for Dynkin quivers
Creators: Yariana Diaz
Cody Gilbert
Ryan Kinser
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.2208.02445
ISSN: 2331-8422
Language: English
Date posted: 08/04/2022
Academic Unit: Mathematics
Record Identifier: 9984281629002771

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