Mathematical Sciences: Representation Theory of Infinite Dimensional Lie Algebras and Application

数学科学：无限维李代数表示论及其应用

• 批准号: 9103732
• 负责人: Victor Kac
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103732&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Infinite

This research is concerned with a variety of problems in the representation theory of infinite dimensional Lie algebras. The principal investigator will work on modular invariant representations, exceptional hierarchies of soliton equations, reciprocity laws and infinite-dimensional groups, classification of graded simple Lie super-algebras of growth 1, and quantum groups. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of infinite dimensional Lie algebras. The study of these algebras has applications throughout mathematics and mathematical physics.

本研究涉及无限维李代数表示理论中的各种问题。主要的研究人员将致力于模不变表示、孤子方程的例外层次、互易定律和无限维群、增长的分次单李超代数的分类以及量子群。许多不同的代数对象可以表示为其他代数对象的代数变换集。通过这些表示法可以确定它们的结构。本课题主要研究无限维李代数的表示理论。对这些代数的研究在整个数学和数学物理中都有应用。