An explicit construction of simple-minded systems over self-injective Nakayama algebras

TL;DR

This paper provides an explicit method to construct simple-minded systems in the stable module categories of self-injective Nakayama algebras, building on recent characterizations of orthogonal systems.

Contribution

It introduces a new explicit construction technique for simple-minded systems specifically over self-injective Nakayama algebras, expanding understanding of their stable categories.

Findings

Explicit construction method for simple-minded systems

Application of recent orthogonal system characterization

Enhanced understanding of stable module categories

Abstract

Recently, we obtained in [7] a new characterization for an orthogonal system to be a simple-minded system in the stable module category of any representation-finite self-injective algebra. In this paper, we apply this result to give an explicit construction of simple-minded systems over self-injective Nakayama algebras.