Lattice structure of torsion classes for hereditary artin algebras

2014/02/06 by Claus Michael Ringel, Ringel, Claus Michael
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1402.1260

arxiv created 2014/02/06 · arxiv updated 2014/02/07

Abstract

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.

Related

• Dynamical Combinatorics and Torsion Classes
• Representation theory of hereditary artin algebras of finite representation type
• An introduction to the lattice of torsion classes
• Ideal Torsion Pairs for Artin Algebras
• A remark on s-torsion pairs and on the lattice of Dyck paths