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arXiv · 2110.02777

The Auslander-Reiten quivers of string algebras of affine type $\widetilde{C}$ and a conjecture by Geiss-Leclerc-Schröer

Hua-Lin Huang·Zengqiang Lin·Xiuping Su
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Abstract

In this paper, we study representations of certain string algebras, which are referred to as of affine type $\widetilde{C}$. We introduce minimal string modules and apply them to explicitly describe components of the Auslander-Reiten quivers of the string algebras and $τ$-locally free modules defined by Geiss-Lerclerc-Schröer. As an application, we prove Geiss-Leclerc-Schröer's conjecture on the correspondence between positive roots of type $\widetilde{C}$ and $τ$-locally free modules of the corresponding string algebras.

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Hua-Lin Huang, Zengqiang Lin, Xiuping Su. 2021-11-16. The Auslander-Reiten quivers of string algebras of affine type $\widetilde{C}$ and a conjecture by Geiss-Leclerc-Schröer. https://arxiv.org/abs/2110.02777

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