Mathematical Sciences: Cohomology and Representation Theory of Algebraic Groups and Lie Algebras

数学科学：代数群和李代数的上同调和表示论

• 批准号: 9500715
• 负责人: Daniel Nakano
• 金额: $ 5.91万
• 依托单位: Utah State University
• 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: 1995-09-15 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500715&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Representation; Theory

This project is concerned with the representation theory of algebraic groups and Lie algebras. The spectrum of the cohomology ring will be a fundamental object of interest. This will enable the principal investigator to apply methods from algebraic geometry and algebraic topology in order to understand the representation/cohomology theory of these groups and algebras. The research supported concerns the representation theory of various algebraic objects including algebraic groups and Lie algebras. Representation theory is an important method for determining the structure of these objects. This work has important implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.

该项目与代数群体的表示理论和代数有关。 共同学环的频谱将是感兴趣的基本对象。 这将使主要研究者能够应用代数几何形状和代数拓扑的方法，以了解这些群体和代数的表示/同谋理论。 该研究支持的涉及各种代数对象的表示理论，包括代数群体和代数为代数。 表示理论是确定这些对象结构的重要方法。 这项工作对许多数学领域具有重要意义，包括环理论，群体理论，拓扑和谎言代数研究。