Quivers with relations arising from clusters (An case). Transaction od AMS
by
P. Caldero
,
F. Chapoton
,
R. Schiffler
| Citations: | 70 - 13 self |
BibTeX
@MISC{Caldero_quiverswith,
author = {P. Caldero and F. Chapoton and R. Schiffler},
title = {Quivers with relations arising from clusters (An case). Transaction od AMS},
year = {}
}
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Abstract
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type An. We associate to each cluster C of U an abelian category CC such that the indecomposable objects of CC are in natural correspondence with the cluster variables of U which are not in C. We give an algebraic realization and a geometric realization of CC. Then, we generalize the “denominator Theorem ” of Fomin and Zelevinsky to any cluster. 0
Citations
| 255 | Representation theory of Artin algebras - Auslander - 1974 |
| 50 | Cluster algebras III: Upper bounds and double Bruhat cells - Berenstein, Fomin, et al. |
| 48 | Auslander-Reiten sequences and representation-finite algebras - Gabriel - 1979 |
| 45 | Generalized associahedra via quiver representations - Marsh, Reineke, et al. |
| 41 | Tilting theory and cluster combinatorics - Buan, Marsh, et al. |
| 38 | Y-systems and generalized associahedra - Fomin, Zelevinsky |
| 8 | Finite type classification - algebras |
