论文标题
通过反射的本地免费Caldero-chapoton功能
Locally free Caldero-Chapoton functions via reflections
论文作者
论文摘要
我们研究了与Geiss-Leclerc-Schröer的表示相关的局部自由caldero-chapoton函数的反射，这些函数与可对称的Cartan矩阵的关系有关。我们证明，对于等级2群集代数，非初始群集变量表示为本地不可分解的刚性刚性表示的本地游离caldero-chapoton函数。我们的方法产生了新证明，证明了Geiss-Leclerc-Schröer在Dynkin案例中获得的本地自由Caldero-chapoton公式。对于一般的无环偏度 - 对称性群集代数，我们证明了通过几乎下沉和源突变获得的任何非初始群集变量的公式。
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.
