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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-Schr\"{o}er

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 $\tau$-locally free modules defined by Geiss-Lerclerc-Schr\"{o}er. As an application, we prove Geiss-Leclerc-Schr\"{o}er's conjecture on the correspondence between positive roots of type $\widetilde{C}$ and $\tau$-locally free modules of the corresponding string algebras.

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Hua-Lin Huang, Zengqiang Lin, Xiuping Su. 2021-10-06. The Auslander-Reiten quivers of string algebras of affine type $\widetilde{C}$ and a conjecture by Geiss-Leclerc-Schr\"{o}er. https://arxiv.org/abs/2110.02777

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