Maximal rigid subcategories and cluster-tilting subcategories in 2-CY categories

被引：0
|
作者：
Xu, Jinde [1 ]
Ouyang, Baiyu [2 ]
机构：
[1] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada
[2] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2017年 / 473卷
关键词：
2-CY triangulated categories; Cluster-tilting subcategories; Maximal rigid subcategories; 2-CALABI-YAU CATEGORIES;
D O I：
10.1016/j.jalgebra.2016.10.030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let C be a connected Horn-finite 2-CY triangulated category. We prove that if T is a functorially finite maximal rigid subcategory of C without loops in its quiver, then T is cluster-tilting. In particular, this gives a positive answer to a conjecture proposed in [5]. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：183 / 193
页数：11
相关论文
共 50 条
  • [1] CLUSTER-TILTING SUBCATEGORIES IN EXTRIANGULATED CATEGORIES
    Zhou, Panyue
    Zhu, Bin
    THEORY AND APPLICATIONS OF CATEGORIES, 2019, 34 : 221 - 242
  • [2] Maximal rigid objects without loops in connected 2-CY categories are cluster-tilting objects
    Xu, Jinde
    Ouyang, Baiyu
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (05)
  • [3] TRIANGULATED CATEGORIES WITH CLUSTER TILTING SUBCATEGORIES
    Yang, Wuzhong
    Zhou, Panyue
    Zhu, Bin
    PACIFIC JOURNAL OF MATHEMATICS, 2019, 301 (02) : 703 - 740
  • [4] Quotients of exact categories by cluster tilting subcategories as module categories
    Demonet, Laurent
    Liu, Yu
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (12) : 2282 - 2297
  • [5] dZ-Cluster tilting subcategories of singularity categories
    Kvamme, Sondre
    MATHEMATISCHE ZEITSCHRIFT, 2021, 297 (1-2) : 803 - 825
  • [6] Abelian Categories Arising from Cluster Tilting Subcategories
    Yu Liu
    Panyue Zhou
    Applied Categorical Structures, 2020, 28 : 575 - 594
  • [7] Abelian Categories Arising from Cluster Tilting Subcategories
    Liu, Yu
    Zhou, Panyue
    APPLIED CATEGORICAL STRUCTURES, 2020, 28 (04) : 575 - 594
  • [8] ∞-Tilting Subcategories in Extriangulated Categories
    Zhang, Zhen
    Wei, Jiaqun
    Wang, Shance
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2024, 45 (01) : 151 - 160
  • [9] ∞-Tilting Subcategories in Extriangulated Categories
    Zhen ZHANG
    Jiaqun WEI
    Shance WANG
    Chinese Annals of Mathematics,Series B, 2024, (01) : 151 - 160
  • [10] Rigid subcategories and related subcategories in extriangulated categories
    Zhang, Zhen
    Wang, Shance
    COMMUNICATIONS IN ALGEBRA, 2023, 51 (11) : 4804 - 4814
12345