Quivers with relations arising from clusters (A_n case)
表示论
2014-04-09 v1 环与代数
摘要
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.
引用
@article{arxiv.math/0401316,
title = {Quivers with relations arising from clusters (A_n case)},
author = {Philippe Caldero and Frederic Chapoton and Ralf Schiffler},
journal= {arXiv preprint arXiv:math/0401316},
year = {2014}
}
备注
18 pages, 6 figures