From triangulated categories to cluster algebras II

被引：159

作者：

Caldero, Philippe ^{[1
]}

Keller, Bernhard

机构：

[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Univ Paris 7 Denis Diderot, Inst Math, F-75251 Paris 05, France

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2006年 / 39卷 / 06期

关键词：

D O I：

10.1016/j.ansens.2006.09.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator theorem, and some conjectures on properties of the mutation graph. As in the previous article, the proofs rely on the Calabi-Yau property of the cluster category. (c) 2006 Elsevier Masson SAS.

引用

页码：983 / 1009

页数：27

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