Semi-stable subcategories for Euclidean quivers

Ingalls, Colin; Paquette, Charles et Thomas, Hugh (2015). « Semi-stable subcategories for Euclidean quivers ». Proceedings of the London Mathematical Society, 110(4), pp. 805-840.

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Résumé

In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to the Dynkin case, we find out that the intersection of semi-stable subcategories may not be semi-stable. However, only a finite number of exceptions occur, and we give a description of these subcategories. Moreover, one can attach a simplicial complex to any acyclic quiver Q, and this simplicial complex allows one to completely determine the canonical decomposition of any dimension vector. This simplicial complex has a nice description in the Euclidean case: it is described using an arrangement of convex pieces of hyperplanes, each piece being indexed by a real Schur root or a set of quasi-simple objects.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Associative rings and algebras, Representation theory of rings and algebras, Representations of quivers and partially ordered sets
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Hugh R. Thomas
Date de dépôt:	18 mai 2016 19:50
Dernière modification:	30 mai 2016 20:14
Adresse URL :	http://archipel.uqam.ca/id/eprint/8488

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