ON THE MODULE CATEGORIES OF GENERALIZED PREPROJECTIVE ALGEBRAS OF DYNKIN TYPE

Abstract

For a symmetrizable GCM C and its symmetrizer D, Geiss-Leclerc-Schr¨oer [Invent. Math. 209 (2017)] has introduced a generalized preprojective algebra Π associated to C and D, that contains a class of modules, called locally free modules. We show that any basic support τ- tilting Π-module is locally free and gives a classification theorem of torsion-free classes in repΠ as the generalization of the work of Mizuno [Math. Z. 277 (2014)]