Mathematical Sciences: Representations & Cohomology of Finite & Compact Lie Groups

数学科学：表示

• 批准号: 9401004
• 负责人: David Benson
• 金额: $ 10.05万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401004&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representations; & Cohomology

Benson This award supports work on representations and cohomology of finite and compact Lie groups. There are three areas which will be investigated. The first is an investigation of the representation theory and cohomology of finite groups, primarily over fields of prime characteristic. The second involves understanding the cohomology of compact Lie groups, by extending current methods from the finite case. The third is aimed at constructing maps between classifying spaces of finite and compact Lie groups. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups. ***

本森奖支持在有限紧李群的表示和上同调方面的工作。将对三个领域进行调查。第一个是关于有限群的表示理论和上同调的研究，主要是关于素特征域。第二个涉及通过从有限情形扩展现有方法来理解紧李群的上同调。第三个目的是构造有限李群和紧李群的分类空间之间的映射。所支持的研究涉及有限群的表示理论。群是用于研究变换的代数对象。正因为如此，小组是物理、化学和计算机科学以及数学中的基本工具。表象理论是确定群结构的重要方法。***