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.

10 pages. Minor errors are corrected, and references are updated in the second version