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 ...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.展开更多
We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior alge...We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.展开更多
基金Supported partially by the National 973 Programs (Grant No. 2006CB805905)
文摘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.
基金NSFC#10371036,SRFDP#200505042004 the Cultivation Fund of the Key ScientificTechnical Innovation Project #21000115 of the Ministry of Education of China
文摘We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.
