从Orbifolds上得到的簇代数的基

三角剖分轨形产生的蛇图与 Caldero–Chapoton 函数

Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds

本文证明三角剖分轨形中弧、闭曲线对应的 Caldero–Chapoton 函数与蛇图展开一致，并由此建立温和代数不可分解模与广义丛代数丛变量间的双射。

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 reachable $τ$-rigid pairs and cluster monomials of the generalized cluster algebra associated to the surface by Chekhov and Shapiro.

Orbifold diagrams

We study alternating strand diagrams on the disk with an orbifold point. These are quotients by rotation of Postnikov diagrams on the disk, and we call them orbifold diagrams. We associate a quiver with potential to each orbifold diagram, in such a way that its Jacobian algebra and the one associated to the covering Postnikov diagram are related by a skew-group algebra construction. We moreover realise this Jacobian algebra as the endomorphism algebra of a certain explicit cluster-tilting object. This is similar to (and relies on) a result by Baur-King-Marsh for Postnikov diagrams on the disk.

簇代数与闭轨道面关联的极大绿色序列

Maximal Green Sequences for Cluster Algebras Associated to Closed Orbifolds

本文研究了闭轨道面关联的簇代数中极大绿色序列的存在条件，通过构造三角剖分来确定其存在性。

簇代数与三角化orbifold

Cluster algebras and triangulated orbifolds

将Fomin和Thurston的理论推广到斜对称化情形，构造了非例外突变有限簇代数的几何实现。这些代数的簇变量是某些双曲orbifolds上的重整化λ长度。我们还计算了这些簇代数的增长率，给出了簇变量的Laurent展开式的正性，并证明了c-向量的符号相干性。

The Large $N$ Limit of Orbifold Vertex Operator Algebras

We investigate the large $N$ limit of permutation orbifolds of vertex operator algebras. To this end, we introduce the notion of nested oligomorphic permutation orbifolds and discuss under which conditions their fixed point VOAs converge. We show that if this limit exists, then it has the structure of a vertex algebra. Finally, we give an example based on $\mathrm{GL}(N,q)$ for which the fixed point VOA limit is also the limit of the full permutation orbifold VOA.

格顶点算子代数的循环轨道折叠的额外自同构

Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras

本文研究了无根偶格顶点算子代数在奇素数阶无不动点等距提升下的循环轨道折叠自同构群，证明了额外自同构存在的充要条件是该格由 Construction B 构造或同构于 Leech 格的余不变格。

Deligne-Lusztig 变量、托里克轨道与 q-Klyachko 代数

Deligne--Lusztig varieties, toric orbifolds, and the $q$-Klyachko algebra

研究 q-Klyachko 代数的几何结构，当 q 为素数幂时，证明其为 Chow 环上的拉回映射像；当 q 为正有理数时，通过 toric 几何建立其 Kahler 包装。

来自穿孔轨形体的簇展开

Cluster Expansions from Punctured Orbifolds

本文给出了与穿孔轨形体上弧相关的广义簇代数元素的多重组合展开公式，包括蛇形图、标记偏序集、矩阵和T-游走，并证明了它们的等价性，统一并推广了现有结果。