GIT-equivalence and semi-stable subcategories of quiver representations

In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14]. Here we take a more invariant theoretic appro...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 223; no. 8; pp. 3499 - 3514
Main Authors Chindris, Calin, Granger, Valerie
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2019
Subjects
GIT-cones
Schur roots
Semi-stable quiver representations
Tame quivers
13A50
GIT-cones
Tame quivers
Schur roots
Semi-stable quiver representations
16G20
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Summary:In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14]. Here we take a more invariant theoretic approach, to answer this question in general. We recover the known result in the tame case.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.11.014