On the module categories of generalized preprojective algebras of Dynkin type

Abstract

For a symmetrizable GCM $C$ and its symmetrizer $D$, Geiss-Leclerc-Schröer [Invent. Math. 209 (2017)] has introduced a generalized preprojective algebra $\Pi$ associated to $C$ and $D$, that contains a class of modules, called locally free modules. We show that any basic support $\tau$-tilting $\Pi$-module is locally free and gives a classification theorem of torsion-free classes in $\mathrm{rep}\Pi$ as the generalization of the work of Mizuno [Math. Z. 277 (2014)].

arXiv comment17 pages; v3: final version, slightly changed the title