Coxeter combinatorics and cluster algebras
Coxeter 组合数学和簇代数
基本信息
- 批准号:1101568
- 负责人:
- 金额:$ 13.5万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-08-01 至 2015-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Cluster algebras were introduced by S. Fomin and A. Zelevinsky as a framework for studying total positivity and canonical bases in semisimple groups. They have since appeared in a wide range of mathematical areas, including Teichmüller theory, Poisson geometry, quiver representations, Lie theory, algebraic geometry, algebraic combinatorics, and even in partial differential equations (in the equations describing shallow water waves). This project will bring new Coxeter-theoretic tools to bear on the study of cluster algebras, in order to greatly expand the class of well-understood cluster algebras, and to prove new results even in finite type. Much of the research will use the combinatorics and geometry of sortable elements and Cambrian fans, developed by the investigator in collaboration with D. Speyer.This project brings together two streams of mathematical research that both have deep connections to a broad array of mathematical fields. Coxeter groups are an algebraic abstraction based on reflective symmetry, and they have played a role in some of the important mathematical developments of the past century. Cluster algebras are a more recent discovery, but have already shown surprising applications in unexpected areas. The application of Coxeter-theoretic tools is one of several promising approaches to the structural study of cluster algebras. The interaction also goes in the other direction, as cluster algebras bring to light new ways of understanding Coxeter groups.
簇代数是由S. Fomin和A. Zelevinsky作为一个框架,研究总的积极性和典型的基础,在半单群。 它们已经出现在广泛的数学领域,包括泰希米勒理论,泊松几何,代数表示,李理论,代数几何,代数组合学,甚至在偏微分方程(在方程描述浅水波)。 这个项目将带来新的Coxeter理论工具,承担对集群代数的研究,以大大扩大类的理解集群代数,并证明新的结果,即使在有限型。 大部分研究将使用可排序元素和寒武纪风扇的组合学和几何学,由研究人员与D。该项目汇集了两个数学研究流,两者都与广泛的数学领域有着深刻的联系。 考克斯特群是一种基于反射对称性的代数抽象,它们在过去世纪的一些重要数学发展中发挥了作用。 簇代数是最近的发现,但已经在意想不到的领域显示出令人惊讶的应用。 Coxeter理论工具的应用是研究簇代数结构的几种有前途的方法之一。 这种相互作用也朝着另一个方向发展,因为簇代数揭示了理解考克斯特群的新方法。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Nathan Reading其他文献
Lattice congruences, fans and Hopf algebras
格同余、扇形和 Hopf 代数
- DOI:
10.1016/j.jcta.2004.11.001 - 发表时间:
2004 - 期刊:
- 影响因子:0
- 作者:
Nathan Reading - 通讯作者:
Nathan Reading
Noncrossing Arc Diagrams and Canonical Join Representations
非交叉弧图和规范连接表示
- DOI:
10.1137/140972391 - 发表时间:
2014 - 期刊:
- 影响因子:0
- 作者:
Nathan Reading - 通讯作者:
Nathan Reading
Order Dimension, Strong Bruhat Order and Lattice Properties for Posets
阶数维数、强 Bruhat 阶数和偏序集的晶格性质
- DOI:
- 发表时间:
2002 - 期刊:
- 影响因子:0.4
- 作者:
Nathan Reading - 通讯作者:
Nathan Reading
Cambrian frameworks for cluster algebras of affine type
仿射型簇代数的寒武纪框架
- DOI:
- 发表时间:
2015 - 期刊:
- 影响因子:0
- 作者:
Nathan Reading;David E. Speyer - 通讯作者:
David E. Speyer
Lattice Congruences of the Weak Order
弱阶格同余
- DOI:
10.1007/s11083-005-4803-8 - 发表时间:
2004 - 期刊:
- 影响因子:0.4
- 作者:
Nathan Reading - 通讯作者:
Nathan Reading
Nathan Reading的其他文献
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{{ truncateString('Nathan Reading', 18)}}的其他基金
Coxeter Groups, Scattering Diagrams, and Shards
Coxeter 组、散点图和碎片
- 批准号:
2054489 - 财政年份:2021
- 资助金额:
$ 13.5万 - 项目类别:
Continuing Grant
Combinatorics and geometry of mutations
突变的组合学和几何学
- 批准号:
1500949 - 财政年份:2015
- 资助金额:
$ 13.5万 - 项目类别:
Continuing Grant
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