Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules. For the case of A being the path algebra of a quiver, this result has recently been established by Iyama-Reiten-Thomas-Todorov and our proof follows closely their considerations.
The number of simple modules for the Hecke algebras of type G(r,p,n) (with an appendix by Xiaoyi Cui)
Vertices of simple modules of symmetric groups labelled by hook partitions
Weyl submodules in restrictions of simple modules
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