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Stability spaces of string and band modules

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Stability spaces of string and band modules. / Schroll, Sibylle; Tattar, Aran; Treffinger, Hipolito et al.
In: Journal of Pure and Applied Algebra, Vol. 228, No. 4, 107503, 30.04.2024.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Schroll, S, Tattar, A, Treffinger, H, Valdivieso, Y & Williams, NJ 2024, 'Stability spaces of string and band modules', Journal of Pure and Applied Algebra, vol. 228, no. 4, 107503. https://doi.org/10.1016/j.jpaa.2023.107503

APA

Schroll, S., Tattar, A., Treffinger, H., Valdivieso, Y., & Williams, N. J. (2024). Stability spaces of string and band modules. Journal of Pure and Applied Algebra, 228(4), Article 107503. https://doi.org/10.1016/j.jpaa.2023.107503

Vancouver

Schroll S, Tattar A, Treffinger H, Valdivieso Y, Williams NJ. Stability spaces of string and band modules. Journal of Pure and Applied Algebra. 2024 Apr 30;228(4):107503. Epub 2023 Aug 24. doi: 10.1016/j.jpaa.2023.107503

Author

Schroll, Sibylle ; Tattar, Aran ; Treffinger, Hipolito et al. / Stability spaces of string and band modules. In: Journal of Pure and Applied Algebra. 2024 ; Vol. 228, No. 4.

Bibtex

@article{156c49e330d1454d9be22e12d8f2b613,
title = "Stability spaces of string and band modules",
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.",
keywords = "Stability conditions, String modules, Band modules, Special biserial algebras, Cones, Order polytopes",
author = "Sibylle Schroll and Aran Tattar and Hipolito Treffinger and Yadira Valdivieso and Williams, {Nicholas J.}",
year = "2024",
month = apr,
day = "30",
doi = "10.1016/j.jpaa.2023.107503",
language = "English",
volume = "228",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Stability spaces of string and band modules

AU - Schroll, Sibylle

AU - Tattar, Aran

AU - Treffinger, Hipolito

AU - Valdivieso, Yadira

AU - Williams, Nicholas J.

PY - 2024/4/30

Y1 - 2024/4/30

N2 - 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.

AB - 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.

KW - Stability conditions

KW - String modules

KW - Band modules

KW - Special biserial algebras

KW - Cones

KW - Order polytopes

U2 - 10.1016/j.jpaa.2023.107503

DO - 10.1016/j.jpaa.2023.107503

M3 - Journal article

VL - 228

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

M1 - 107503

ER -