Self-injective algebras under derived equivalences

被引：0
|
作者：
Xi, Changchang [1 ,2 ]
Zhang, Jin [1 ]
机构：
[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[2] Shaanxi Normal Univ, Sch Math & Stat, Xian 710119, Peoples R China
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2025年 / 229卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Derived equivalence; Grothendieck group; Nakayama permutation; Self-injective algebra; Symmetric algebra; Weakly symmetric algebra;
D O I：
10.1016/j.jpaa.2024.107795
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
引用
收藏
页数：11
相关论文
共 50 条
  • [21] TTF Theories Induced by Two-Term Tilting Complexes and Self-Injective Algebras
    Abe, Hiroki
    ALGEBRAS AND REPRESENTATION THEORY, 2023, 26 (06) : 2467 - 2483
  • [22] THE COMPONENT QUIVER OF A SELF-INJECTIVE ARTIN ALGEBRA
    Jaworska, Alicja
    Skowronski, Andrzej
    COLLOQUIUM MATHEMATICUM, 2011, 122 (02) : 233 - 239
  • [23] A Note on Derived Equivalences for Φ-Green Algebras
    Shengyong Pan
    Zhen Peng
    Algebras and Representation Theory, 2014, 17 : 1707 - 1720
  • [24] Derived equivalences for hereditary Artin algebras
    Stanley, Donald
    van Roosmalen, Adam-Christiaan
    ADVANCES IN MATHEMATICS, 2016, 303 : 415 - 463
  • [25] Constructions of derived equivalences for algebras and rings
    Changchang Xi
    Frontiers of Mathematics in China, 2017, 12 : 1 - 18
  • [26] Constructions of derived equivalences for algebras and rings
    Xi, Changchang
    FRONTIERS OF MATHEMATICS IN CHINA, 2017, 12 (01) : 1 - 18
  • [27] Self-injective Cellular Algebras Whose Representation Type are Tame of Polynomial Growth (vol 23, pg 833, 2020)
    Ariki, S.
    Kase, R.
    Miyamoto, K.
    Wada, K.
    ALGEBRAS AND REPRESENTATION THEORY, 2020, 23 (03) : 873 - 874
  • [28] A Note on Derived Equivalences for I¦-Green Algebras
    Pan, Shengyong
    Peng, Zhen
    ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (06) : 1707 - 1720
  • [29] DERIVED EQUIVALENCES FOR Φ-AUSLANDER-YONEDA ALGEBRAS
    Hu, Wei
    Xi, Changchang
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (11) : 5681 - 5711
  • [30] Derived Equivalences Between Generalized Matrix Algebras
    QingHua Chen
    HongJin Liu
    Czechoslovak Mathematical Journal, 2020, 70 : 147 - 160
12345