A Note on Singularity Categories and Triangular Matrix Algebras

被引：0
作者：
Qin, Yongyun [1 ]
机构：
[1] Yunnan Normal Univ, Sch Math, Kunming 650500, Yunnan, Peoples R China
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2024年 / 27卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Singularity category; Triangular matrix algebra; Gorenstein defect category; Recollement; GORENSTEIN-PROJECTIVE-MODULES; RECOLLEMENTS; EQUIVALENCES;
D O I：
10.1007/s10468-023-10249-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Lambda = [(A 0) (M B)] be an Artin algebra and M-B(A) a B-A-bimodule. We prove that there is a triangle equivalence D-sg(Lambda) congruent to D-sg(A) coproduct D-sg(B) between the corresponding singularity categories if BM is semi-simple and M-A is projective. As a result, we obtain a new method for describing the singularity categories of certain bounded quiver algebras.
引用
收藏
页码：1111 / 1119
页数：9
相关论文
共 34 条
  • [1] [Anonymous], 1988, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras
  • [2] Barrios M, 2023, ALGEBR REPRESENT TH, V26, P3255, DOI 10.1007/s10468-023-10218-w
  • [3] On algebras of On-finite and O8-infinite representation type
    Barrios, Marcos
    Mata, Gustavo
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (11)
  • [4] Beilinson A. A., 1982, FAISCEAUX PERVERS AS
  • [5] Beilinson AA., 1988, J GEOM PHYS, V5, P317
  • [6] THE GORENSTEIN DEFECT CATEGORY
    Bergh, Petter Andreas
    Oppermann, Steffen
    Jorgensen, David A.
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2015, 66 (02) : 459 - 471
  • [7] Buchweitz R.- O., 1986, Maximal Cohen-Macaulay modules and Tatecohomology over Gorenstein rings
  • [8] The Gorenstein-projective modules over a monomial algebra
    Chen, Xiao-Wu
    Shen, Dawei
    Zhou, Guodong
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2018, 148 (06) : 1115 - 1134
  • [9] THE SINGULARITY CATEGORY OF A QUADRATIC MONOMIAL ALGEBRA
    Chen, Xiao-Wu
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2018, 69 (03) : 1015 - 1033
  • [10] SINGULAR EQUIVALENCES INDUCED BY HOMOLOGICAL EPIMORPHISMS
    Chen, Xiao-Wu
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (08) : 2633 - 2640
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