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.

恩莱特将研究李代数的表示理论 定义在交换环上， 特殊的极大理想是proscription，其剩余 字段是复数。 特别值得关注的是， 定义在环上的李代数的水平上的信息产生 对于更传统的李代数来说， 通过从环到环的通道， 剩余域 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身，特别是在分析和数字方面， 理论和理论物理学，特别是量子 力学和基本粒子物理学。