Applications of Representation Theory in Commutative Algebra

表示论在交换代数中的应用

• 批准号: 1802067
• 负责人: Jerzy Weyman
• 金额: $ 28.2万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1802067&HistoricalAwards=false
• 关键词: Applications; Representation; Theory; Commutative; Algebra

This project involves the study of problems from several branches of algebra. Commutative algebra studies sets defined by polynomial equations. The first and second part of the project are devoted to studying polynomial equations defining certain sets characterized geometrically. The third part of this project will be a systematic study of certain kinds of graphs from a geometric point of view.This project consists of several interrelated parts. The first part is to study the structure of generic rings for finite free resolutions. The principal investigator proposes to develop his discovery of a link between the generic ring for resolutions of length 3 and Kac-Moody Lie algebras related to T-shaped graphs. The second part is related to calculating local cohomology. The PI plans to develop his calculation of local cohomology for certain classes of commutative rings. The third part involves several other projects on noncommutative algebra. The PI will study picture groups defined for modulated quivers and the geometry of the components of representation spaces for quivers with relations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目涉及代数几个分支的问题的研究。交换代数研究由多项式方程定义的集合。该项目的第一和第二部分致力于研究多项式方程定义某些集的几何特征。本计画的第三部分将从几何的观点来系统地研究某些种类的图。本计画由几个相互关联的部分组成。第一部分是研究有限自由分解的一般环的结构。首席研究员建议发展他的发现之间的联系通用环的决议长度为3和卡茨穆迪李代数有关的T形图。第二部分是关于局部上同调的计算。PI计划发展他的计算局部上同调的某些类别的交换环。 第三部分涉及非交换代数的其他几个项目。PI将研究为调制颤动定义的图片组以及具有关系的颤动的表示空间组件的几何形状。该奖项反映了NSF的法定使命，并且通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

项目成果

Some branching formulas for Kac-Moody Lie algebras

Kac-Moody 李代数的一些分支公式

• DOI: 10.4134/ckms.c180373
• 发表时间: 2019
• 期刊: Daehan suhaghoe nonmunjib
• 作者: Lee, Kyu-Hwan;Weyman, Jerzy
• 通讯作者: Weyman, Jerzy

The family of perfect ideals of codimension 3, of type 2 with 5 generators

余维 3 的完美理想族，类型 2，有 5 个发电机

• DOI: 10.1090/proc/14646
• 发表时间: 2020
• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: Celikbas, Ela;Jai, Laxmi;Kraskiewicz, Witold;Weyman, Jerzy
• 通讯作者: Weyman, Jerzy

Free resolutions of orbit closures of Dynkin quivers

Dynkin 箭袋轨道闭合的自由分辨率

• DOI: 10.1090/tran/7697
• 发表时间: 2019
• 期刊: Transactions of the American Mathematical Society
• 影响因子: 1.3
• 作者: Lorincz, Andras;Weyman, Jerzy
• 通讯作者: Weyman, Jerzy