Maximal rigid objects without loops in connected 2-CY categories are cluster-tilting objects

被引：3
|
作者：
Xu, Jinde [1 ]
Ouyang, Baiyu [1 ]
机构：
[1] Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 05期
关键词：
Cluster-tilting objects; maximal rigid objects; 2-CY categories; 2-CALABI-YAU CATEGORIES; ALGEBRAS; MUTATION; MODULES;
D O I：
10.1142/S0219498815500711
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study Conjecture II. 1.9 of [A. B. Buan, O. Iyama, I. Reiten and J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups, Compos. Math. 145(4) (2009) 1035-1079], which said that any maximal rigid object without loops or 2-cycles in its quiver is a cluster-tilting object in a connected Hom-finite triangulated 2-CY category C. We obtain some conditions equivalent to the conjecture, and by using them we prove the conjecture.
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页数：13
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