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 $\operatorname{\mathbf{rep}}{\Pi}$ as the generalization of the work of Mizuno [Math. Z. 277 (2014)].
Acknowledgments
The author thanks his supervisor Syu Kato for hopeful encouragement and pointing out of many typographical errors of a draft of this paper. The author also thanks Bernard Leclerc for telling him an easy proof of Theorem 3.4 and giving him many interesting lectures about this topic during his stay in Kyoto. Finally, the author thanks the referee for carefully reading the manuscript and for giving constructive comments.
Citation
Kota Murakami. "On the module categories of generalized preprojective algebras of Dynkin type." Osaka J. Math. 59 (2) 387 - 402, April 2022.
Information
