Quivers with relations arising from clusters $(A_n$ case)
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- by P. Caldero, F. Chapoton and R. Schiffler PDF
- Trans. Amer. Math. Soc. 358 (2006), 1347-1364 Request permission
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 $A_n$. We associate to each cluster $C$ of $U$ an abelian category $\mathcal {C}_C$ such that the indecomposable objects of $\mathcal {C}_C$ 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 $\mathcal {C}_C$. Then, we generalize the “denominator theorem” of Fomin and Zelevinsky to any cluster.References
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Additional Information
- P. Caldero
- Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France
- F. Chapoton
- Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France
- R. Schiffler
- Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
- MR Author ID: 724459
- Received by editor(s): February 25, 2004
- Received by editor(s) in revised form: May 24, 2004
- Published electronically: May 26, 2005
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 1347-1364
- MSC (2000): Primary 16G20, 16G70, 05E15, 20F55
- DOI: https://doi.org/10.1090/S0002-9947-05-03753-0
- MathSciNet review: 2187656