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

2019/09/10 by Aaron Chan, Yuming Liu, Chan, Aaron +3
Mathematics · Physics and Astronomy · #16G10 #16G70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum many-body systems #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1909.04440

openalex publication_date 2019/09/10 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

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 \stmodA. We show that the intersection S\capC 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.

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