n-Abelian quotient categories

被引：8
作者：
Zhou, Panyue [1 ]
Zhu, Bin [2 ]
机构：
[1] Hunan Inst Sci & Technol, Coll Math, Yueyang 414006, Hunan, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2019年 / 527卷
关键词：
(n+2)-angulated categories; n-Abelian categories; Cluster-tilting subcategories; n-Gorenstein categories; TRIANGULATED CATEGORIES; CLUSTER; MUTATION;
D O I：
10.1016/j.jalgebra.2019.03.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let C be an (n + 2)-angulated category with an n-suspension functor Sigma(n) and X be a cluster-tilting subcategory of C. Then we show that the quotient category C/X is an n-abelian category, and C/X is equivalent to an n-cluster tilting subcategory of an abelian category mod(Sigma X-n). In addition, if C has a Serre functor, we also prove that mod(Sigma X-n) is Gorenstein of Gorenstein dimension at most n. As an application, we generalize recent results of Jacobsen-Jorgensen and Koenig-Zhu. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：264 / 279
页数：16
相关论文
共 15 条
  • [1] Auslander M., 1966, Proceedings of the Conference Categorical Algebra (La Jolla, Calif., P189
  • [2] The axioms for n-angulated categories
    Bergh, Petter Andreas
    Thaule, Marius
    [J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2013, 13 (04): : 2405 - 2428
  • [3] Buan AB, 2007, T AM MATH SOC, V359, P323
  • [4] n-angulated categories
    Geiss, Christof
    Keller, Bernhard
    Oppermann, Steffen
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 675 : 101 - 120
  • [5] Mutation in triangulated categories and rigid Cohen-Macaulay modules
    Iyama, Osamu
    Yoshino, Yuji
    [J]. INVENTIONES MATHEMATICAE, 2008, 172 (01) : 117 - 168
  • [6] d-abelian quotients of (d+2)-angulated categories
    Jacobsen, Karin M.
    Jorgensen, Peter
    [J]. JOURNAL OF ALGEBRA, 2019, 521 : 114 - 136
  • [7] n-Abelian and n-exact categories
    Jasso, Gustavo
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2016, 283 (3-4) : 703 - 759
  • [8] Torsion Classes and t-Structures in Higher Homological Algebra
    Jorgensen, Peter
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (13) : 3880 - 3905
  • [9] Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
    Keller, Bernhard
    Reiten, Idun
    [J]. ADVANCES IN MATHEMATICS, 2007, 211 (01) : 123 - 151
  • [10] From triangulated categories to abelian categories: cluster tilting in a general framework
    Koenig, Steffen
    Zhu, Bin
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2008, 258 (01) : 143 - 160
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