Quivers with relations arising from clusters (A_n case)

Preprint

23 January 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0401316

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 Cat_C such that the indecomposable objects of Cat_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 Cat_C. Then, we generalize the ``denominator Theorem'' of Fomin and Zelevinsky to any cluster.

Keywords

RELATIONS ARISING
CLUSTER ALGEBRA
ZELEVINSKY
ALGEBRAS
A_N CASE
QUIVERS
CAT_C
FOMIN

All Related Versions

Version 1, 2004-01-23, ArXiv
Published version: Transactions of the American Mathematical Society, 358 (3), 1347.

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