Mathematical Sciences: Representation Theory of Lie Algebras

数学科学：李代数表示论

• 批准号: 9206941
• 负责人: Thomas Enright
• 金额: $ 14.87万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9206941&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Lie

Enright will study the representation theory of Lie algebras defined over a commutative ring in a setting where a distinguished maximal ideal is proscribed for which the residue field is the complex numbers. Of particular interest is whether information at the level of Lie algebras defined over rings yield important information for the more traditional Lie algebras defined over the complex numbers by passage from the ring to the residue field. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

恩莱特将研究在交换环上定义的李代数的表示论，该设置中规定了一个显着的最大理想，其中留数域是复数。 特别令人感兴趣的是，在环上定义的李代数级别的信息是否会通过从环到留数域为在复数上定义的更传统的李代数产生重要信息。 李群理论以挪威数学家索弗斯·李的名字命名，一直是二十世纪数学的主要主题之一。 作为利用系统固有对称性的数学工具，李群的表示论对数学本身（特别是分析和数论）以及理论物理学（特别是量子力学和基本粒子物理学）产生了深远的影响。