Schroll, Sibylle and Tattar, Aran and Treffinger, Hipolito and Valdivieso, Yadira and Williams, Nicholas J. (2024) Stability spaces of string and band modules. Journal of Pure and Applied Algebra, 228 (4): 107503. ISSN 0022-4049
Full text not available from this repository.Abstract
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.