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arXiv · 1906.08739

On the module categories of generalized preprojective algebras of Dynkin type

Kota Murakami
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Abstract

For a symmetrizable GCM $C$ and its symmetrizer $D$, Geiss-Leclerc-Schr\"oer [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)].

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Kota Murakami. 2019-06-20. On the module categories of generalized preprojective algebras of Dynkin type. https://arxiv.org/abs/1906.08739

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