数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1449-1454.doi: 10.1016/S0252-9602(12)60114-3

• 论文 • 上一篇    下一篇

REPETITIVE CLUSTER-TILTED ALGEBRAS

张顺华1|张跃辉2   

  1. 1.School of Mathematics, Shandong University, Jinan 250100, China; 2.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
  • 收稿日期:2010-11-02 修回日期:2011-10-26 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    Supported by the NSF of China (11171183).

REPETITIVE CLUSTER-TILTED ALGEBRAS

 ZHANG Shun-Hua1, ZHANG Yue-Hui2   

  1. 1.School of Mathematics, Shandong University, Jinan 250100, China; 2.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
  • Received:2010-11-02 Revised:2011-10-26 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    Supported by the NSF of China (11171183).

摘要:

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 cluster-tilted 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 CFm, and prove that the tilting graph KCFm of CFm is connected.

关键词: repetitive cluster category, cluster tilting object, repetitive cluster-tilted algebra

Abstract:

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 cluster-tilted 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 CFm, and prove that the tilting graph KCFm of CFm is connected.

Key words: repetitive cluster category, cluster tilting object, repetitive cluster-tilted algebra

中图分类号: 

  • 16G20