Lattice structure of torsion classes for path algebras

Lattice structure of torsion classes for path algebras

Abstract We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices.

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Veröffentlicht in:The Bulletin of the London Mathematical Society 2015-08, Vol.47 (4), p.639-650
Hauptverfasser: Iyama, Osamu, Reiten, Idun, Thomas, Hugh, Todorov, Gordana
Format: Artikel
Sprache:eng
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Zusammenfassung:Abstract We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdv041