The Dimension Vectors of Indecomposable Modules of Cluster-tilted Algebras and the Fomin-Zelevinsky Denominators Conjecture  

作　　者：Shengfei GENG Liangang PENG 

机构地区：[1]Department of Mathematics,Sichuan University

出　　处：《Acta Mathematica Sinica,English Series》2012年第3期581-586,共6页数学学报（英文版）

基　　金：Supported partially by the National 973 Programs (Grant No. 2006CB805905)

摘　　要：The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.

关 键 词：Dimension vector cluster tilting object cluster-tilted algebra denominator 

分 类 号：O152.1[理学—数学]