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

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-09-29 DOI:10.1007/s10468-023-10233-x

Daniel Labardini-Fragoso, Lang Mou

引用次数: 0

Abstract

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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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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.