On the combinatorics of rigid objects in 2-Calabi-Yau categories
| dc.creator | Dehy, Raika | |
| dc.creator | Keller, Bernhard | |
| dc.date | 2007-09-06 | |
| dc.date | 2008-04-14 | |
| dc.date.accessioned | 2026-07-07T09:31:52Z | |
| dc.date.available | 2026-07-07T09:31:52Z | |
| dc.description | Given a triangulated 2-Calabi-Yau category C and a cluster-tilting subcategory T, the index of an object X of C is a certain element of the Grothendieck group of the additive category T. In this note, we show that a rigid object of C is determined by its index, that the indices of the indecomposables of a cluster-tilting subcategory T' form a basis of the Grothendieck group of T and that, if T and T' are related by a mutation, then the indices with respect to T and T' are related by a certain piecewise linear transformation introduced by Fomin and Zelevinsky in their study of cluster algebras with coefficients. This allows us to give a combinatorial construction of the indices of all rigid objects reachable from the given cluster-tilting subcategory T. Conjecturally, these indices coincide with Fomin-Zelevinsky's g-vectors. | |
| dc.description | 11 pages, introduction expanded, references updated, to appear in IMRN | |
| dc.identifier | https://arxiv.org/abs/0709.0882 | |
| dc.identifier | http://arxiv.org/abs/0709.0882 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158613 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 18E30 | |
| dc.title | On the combinatorics of rigid objects in 2-Calabi-Yau categories | |
| dc.type | text |