Affine cluster algebras as dynamical systems, surface triangulations, quiver representations and friezes
仿射簇代数作为动力系统、表面三角测量、箭袋表示和饰带
基本信息
- 批准号:21F20788
- 负责人:
- 金额:$ 0.19万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for JSPS Fellows
- 财政年份:2021
- 资助国家:日本
- 起止时间:2021-04-28 至 2023-03-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The research of the year April 2021 - March 2022 has resulted in the two paperstitled ``~A and ~D type cluster algebras: Triangulated surfaces and friezes'' and ``Period 2 quivers and their T- and Y-systems''. The first of those has been submitted to the Journal of Algebraic Combinatorics, and the corrections have been completed.In the first paper we were able to classify cluster variables for cluster algebras of affine ~A and ~D type. This was done by looking at these cluster variables as arcs of triangulations for appropriate surfaces, a method pioneered in [Fomin, Shapiro and Thurston 2008]. By first identifying the T-system cluster variables and periodic quantities studied in [Fordy and Hone 2014] and [Pallister 2020] as arcs (cluster variables) we were able to identify all other cluster variables in terms of these. We were also able to prove that these cluster variables can be arranged as friezes. Our results agree with similar results found via the representation theory of these quivers. In the second paper we were interested in finding all period 2 quivers. These are quivers that, if mutated twice, look essentially the same. This turned out to be a difficult problem, instead we found all period two quivers with a low number of vertices, of which there are surprisingly many. We then used results of [Nakanishi 2011] to write the T- and Y- systems for these quivers, which here are systems of 2 recurrence relations. We looked at some interesting examples of these which had periodic quantities.
2021年4月至2022年3月的研究已经产生了两篇论文《~A和~D型簇代数:三角化曲面和褶皱》和《周期2箭图及其T-和Y-系》。在第一篇论文中,我们能够对仿射~A和~D类型的簇代数进行分类。这是通过将这些集群变量视为适当表面的三角剖分的弧线来完成的,这是[Fomin,Shapiro和瑟斯顿2008]首创的方法。通过首先将[Fordy and Hone 2014]和[Pallister 2020]中研究的T系统簇变量和周期量识别为圆弧(簇变量),我们能够根据这些识别出所有其他的簇变量。我们还证明了这些星系团变量可以排列成片状。我们的结果与通过这些颤动的表象理论发现的类似结果一致。在第二篇论文中,我们感兴趣的是找出所有周期2的颤动。这些颤动如果突变两次,看起来基本上是一样的。这被证明是一个困难的问题,相反,我们发现所有的周期2箭图的顶点数都很少,令人惊讶的是,顶点数很多。然后我们使用[Nakanishi 2011]的结果来写出这些箭图的T-和Y-系统,这里是2个递归关系的系统。我们看了一些有趣的例子,这些例子都有周期量。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
~A and ~D cluster algebras: Triangulated surfaces, friezes and the cluster category
~A 和 ~D 簇代数:三角曲面、饰带和簇类别
- DOI:
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:Claude Meffan;Amit Banerjee;Jun Hirotani;Toshiyuki Tsuchiya;Joe Pallister
- 通讯作者:Joe Pallister
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
山崎 玲其他文献
フローサイトメトリーを用いたメタン生成菌共生嫌気性繊毛虫の検出と分取
使用流式细胞仪检测和分离产甲烷菌共生厌氧纤毛虫
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
塩浜 康雄;山崎 玲;森 祥太;伊藤 通浩;新里 尚也 - 通讯作者:
新里 尚也
嫌気性繊毛虫GW7株におけるメタン生成アーキア、バクテリアとの共生関係
厌氧纤毛虫GW7菌株中产甲烷古菌与细菌的共生关系
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
竹下和貴;山田尊貴;川原邑斗;成廣 隆;伊藤通浩;鎌形洋一;山崎 玲;新里 尚也 - 通讯作者:
新里 尚也
山崎 玲的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('山崎 玲', 18)}}的其他基金
クラスター代数の組合せ的表現論および可積分系への応用
簇代数的组合表示理论及其在可积系统中的应用
- 批准号:
23K03048 - 财政年份:2023
- 资助金额:
$ 0.19万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
アフィンクラスター代数による力学系、曲面三角形分割、箙表現、およびフリーズの研究
使用仿射簇代数研究动力系统、表面三角测量、颤动表示和冻结
- 批准号:
20F20788 - 财政年份:2020
- 资助金额:
$ 0.19万 - 项目类别:
Grant-in-Aid for JSPS Fellows
Application of cluster algebras to punctured Riemann surfaces and combinatorial representation theory
簇代数在刺穿黎曼曲面和组合表示理论中的应用
- 批准号:
19K03440 - 财政年份:2019
- 资助金额:
$ 0.19万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Conference: 57th Spring Topology and Dynamical Systems Conference
会议:第57届春季拓扑与动力系统会议
- 批准号:
2348830 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant
Conference: 2024 KUMUNU-ISU Conference on PDE, Dynamical Systems and Applications
会议:2024 年 KUMUNU-ISU 偏微分方程、动力系统和应用会议
- 批准号:
2349508 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant
Conference: Second Joint Alabama--Florida Conference on Differential Equations, Dynamical Systems and Applications
会议:第二届阿拉巴马州-佛罗里达州微分方程、动力系统和应用联合会议
- 批准号:
2342407 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant
Collaborative Research: RUI: Wave Engineering in 2D Using Hierarchical Nanostructured Dynamical Systems
合作研究:RUI:使用分层纳米结构动力系统进行二维波浪工程
- 批准号:
2337506 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant
CAREER: Arithmetic Dynamical Systems on Projective Varieties
职业:射影簇的算术动力系统
- 批准号:
2337942 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Continuing Grant
Ergodic theory and multifractal analysis for non-uniformly hyperbolic dynamical systems with a non-compact state space
非紧状态空间非均匀双曲动力系统的遍历理论和多重分形分析
- 批准号:
24K06777 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
CAREER: Solving Estimation Problems of Networked Interacting Dynamical Systems Via Exploiting Low Dimensional Structures: Mathematical Foundations, Algorithms and Applications
职业:通过利用低维结构解决网络交互动力系统的估计问题:数学基础、算法和应用
- 批准号:
2340631 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Continuing Grant
Dynamical Systems with a View towards Applications
着眼于应用的动力系统
- 批准号:
2350184 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Continuing Grant
Conference: Dynamical Systems and Fractal Geometry
会议:动力系统和分形几何
- 批准号:
2402022 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant
Making Upper Division Mathematics Courses More Relevant for Future High School Teachers: The Case of Inquiry-Oriented Dynamical Systems and Modeling
使高年级数学课程与未来高中教师更相关:以探究为导向的动力系统和建模案例
- 批准号:
2337047 - 财政年份:2024
- 资助金额:
$ 0.19万 - 项目类别:
Standard Grant