Torsion pairs and cosilting in type A

Torsion pairs and cosilting in type A

Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new approach to the classification of torsion pairs. In particu...

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Veröffentlicht in:Journal of pure and applied algebra 2022-10, Vol.226 (10), p.107057, Article 107057
Hauptverfasser: Baur, Karin, Laking, Rosanna
Format: Artikel
Sprache:eng
Schlagworte:
Cluster-tilted
Cosilting
Gentle algebra
Geometric model
Pure-injective
Torsion pair
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Zusammenfassung:Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new approach to the classification of torsion pairs. In particular, we classify cosilting modules over cluster-tilted algebras of type A˜. We do this by using a geometric model for finite- and infinite-dimensional modules over such algebras.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2022.107057