Open Access
Translator Disclaimer
April 2022 On the module categories of generalized preprojective algebras of Dynkin type
Kota Murakami
Author Affiliations +
Osaka J. Math. 59(2): 387-402 (April 2022).

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

Download Citation

Kota Murakami. "On the module categories of generalized preprojective algebras of Dynkin type." Osaka J. Math. 59 (2) 387 - 402, April 2022.

Information

Received: 26 October 2020; Revised: 9 February 2021; Published: April 2022
First available in Project Euclid: 7 April 2022

Subjects:
Primary: 16G10
Secondary: 16G20

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.59 • No. 2 • April 2022
Back to Top