Stability spaces of string and band modules

The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from considering the dual description in terms of non-negative linear spans. We show how stability spaces of thin modules are related to order polytopes. In the case of non-thin modules, we show how the stability spaces of string and band modules are related to the stability spaces of the thin modules corresponding to the abstract string and band. We use this to analyse the way in which the stability space of a band module is the limit of stability spaces of string modules. Namely, the stability space of the band module is a union of cones, each of which is the limit of the stability spaces of a family of string modules. & COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

This paper discusses the stability space of modules and its relationship with the dual description in terms of non-negative linear spans. The paper also explores the connection between the stability spaces of thin modules and order polytopes. Additionally, it examines the relationship between the stability spaces of string and band modules and the stability spaces of the corresponding thin modules, as well as the limit of stability spaces of string modules for the stability space of a band module.