REPETITIVE CLUSTER-TILTED ALGEBRAS

doi:10.1016/S0252-9602(12)60114-3

Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1449-1454.doi: 10.1016/S0252-9602(12)60114-3

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REPETITIVE CLUSTER-TILTED ALGEBRAS

ZHANG Shun-Hua¹, ZHANG Yue-Hui²

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).

Abstract

Abstract:

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C_F^m 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

CLC Number:

16G20

ZHANG Shun-Hua, ZHANG Yue-Hui. REPETITIVE CLUSTER-TILTED ALGEBRAS[J].Acta mathematica scientia,Series B, 2012, 32(4): 1449-1454.

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REPETITIVE CLUSTER-TILTED ALGEBRAS

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