On simple-minded systems and τ-periodic modules of self-injective algebras

被引：3

作者：

Chan, Aaron ^{[1
]}

Liu, Yuming ^{[2
]}

Zhang, Zhen ^{[3
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Nagoya, Aichi, Japan

[2] Beijing Normal Univ, Lab Math & Complex Syst, Sch Math Sci, Beijing 100875, Peoples R China

[3] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2020年 / 560卷

关键词：

Simple-minded system; Self-injective algebra; (Stable) Auslander-Reiten quiver; Stably quasi-serial component; Homogeneous tube; AUSLANDER-REITEN COMPONENTS; MUTATIONS;

D O I：

10.1016/j.jalgebra.2020.05.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a finite-dimensional self-injective algebra over an algebraically closed field, C a stably quasi-serial component (i.e. its stable part is a tube) of rank n of the Auslander-Reiten quiver of A, and S be a simple-minded system of the stable module category modA. We show that the intersection S boolean AND C is of size strictly less than n, and consists only of modules with quasi-length strictly less than n. In particular, all modules in the homogeneous tubes of the Auslander-Reiten quiver of A cannot be in any simple-minded system. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：416 / 441

页数：26