Mathematical Sciences: Geometric Aspects of Representationsof Quantum Groups and Kac-Moody Lie Algebras

数学科学：量子群和 Kac-Moody 李代数表示的几何方面

• 批准号: 9501384
• 负责人: Vadim Schechtman
• 金额: $ 8.18万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501384&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Aspects; Representationsof

This award supports research on two main topics: (1) Representations of quantum groups and Kac-Moody Lie algebras and perverse sheaves over configuration spaces; (2) Local structure of moduli spaces. The principal investigator will work on a construction relating certain tensor categories arising from q-deformations of enveloping algebras of simple Lie algebras and certain tensor categories of a geometrical nature. He will also work on describing the completion of the local ring at a point X in terms of the cohomology of certain sheaves of dg Lie algebras over X naturally associated to a deformation problem. This research is concerned with a mathematical object called a Lie algebra. Lie algebras arise from another object called a Lie group. An example of a Lie group is the rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of sperical motion.

该奖项支持两个主要主题的研究：(1)配置空间上的量子群和Kac-Moody李代数的表示以及反层；(2)模空间的局部结构。主要的研究人员将致力于由单李代数的包络代数的q-变形所产生的某些张量范畴与某些具有几何性质的张量范畴之间的关系的构造。他还将致力于用X上某些dg李代数的上同调来描述局部环在点X处的完备性，这些上同调自然地与变形问题相关。这项研究涉及一种名为李代数的数学对象。李代数起源于另一个叫做李群的物体。李群的一个例子是球体的旋转，其中一个旋转之后是另一个旋转。李群和李代数在涉及球面运动分析的领域中很重要。