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arXiv · 2206.02289

Locally free Caldero-Chapoton functions via reflections

Lang Mou
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Abstract

We study the reflections of locally free Caldero-Chapoton functions associated to representations of Geiss-Leclerc-Schröer's quivers with relations for symmetrizable Cartan matrices. We prove that for rank 2 cluster algebras, non-initial cluster variables are expressed as locally free Caldero-Chapoton functions of locally free indecomposable rigid representations. Our method gives rise to a new proof of the locally free Caldero-Chapoton formulas obtained by Geiss-Leclerc-Schröer in Dynkin cases. For general acyclic skew-symmetrizable cluster algebras, we prove the formula for any non-initial cluster variable obtained by almost sink and source mutations.

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Lang Mou. 2023-02-24. Locally free Caldero-Chapoton functions via reflections. https://arxiv.org/abs/2206.02289

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