Lattice structure of torsion classes for path algebras

By Osamu Iyama, I. Reiten, Hugh Thomas, G. Todorov. 2013

55 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/461bd0322a8f9c445139d301f7921a343195c822

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Rowmotion in slow motion (2017, background): “This partial order (torsion pairs, ordered by inclusion of torsion classes; which can also be described as inclusion order on torsion classes) has been considered in [20, 31, 37, 53].”
Lattice Properties of Oriented Exchange Graphs and Torsion Classes (2015, background): “The set of torsion classes of any finite dimensional algebra Λ “ kQ{I is known to form a lattice, and the subposet of functorially finite torsion classes forms a lattice when Λ has certain algebraic properties [20] (we will focus on algebras Λ having finite lattices of torsion classes so we do not n”
Minimal inclusions of torsion classes (2017, background): “ctor D= Hom k( op;k) : mod !mod also furnishes a poset anti-isomorphism from tors to torf op with inverse given by the same duality. (Recall that op denotes the opposite algebra of . For details, see [9] or [13].) Let Sbe a set of indecomposable modules in mod. An S-ltration (of length l) of a modul”