Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and th...Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected.展开更多
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
文摘Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected.
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.
