由具有 3 阶轨道点的曲面产生的温和代数，第一部分：散射图

Pub Date : 2023-09-29 DOI:10.1007/s10468-023-10233-x

Daniel Labardini-Fragoso, Lang Mou

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引用次数: 0

摘要

对于边界上有标记点和三阶轨道点的任何曲面的每个三角剖分，我们都会关联一个带势能的四元组（带环），其雅各布代数是有限维且平缓的。我们研究了这种平缓代数的稳定性散射图，并用它们证明卡尔德罗-查波顿映射定义了 \(\tau \)-刚性对与契科夫和夏皮罗与曲面相关的广义簇代数的簇单项式之间的双射。

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Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams

To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability scattering diagrams of such gentle algebras and use them to prove that the Caldero–Chapoton map defines a bijection between \(\tau \)-rigid pairs and cluster monomials of the generalized cluster algebra associated to the surface by Chekhov and Shapiro.

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