Mathematical Sciences: Structure and Representation Theory of Lie Algebras; April 17-19, 1992, New Haven, CT

数学科学：李代数的结构和表示论；

• 批准号: 9116887
• 负责人: Walter Feit
• 金额: $ 1万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-02-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9116887&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Representation; Theory

The theory of Lie algebras has played a significant role in mathematical research during this century. Important roles have been played by finite-dimensional semisimple Lie algebras, modular Lie algebras and Kac-Moody Lie algebras. The most dramatic progress in the classification and structure of finite dimensional Lie algebras has been the recent solution of the classification problem for simple Lie algebras over algebraically closed fields of characteristic p0. Despite this work, many important areas of research remain, including the characterization of important classes of Lie algebras (e.g., nilpotent, solvable) by homological properties and the search for structural results. There has also been substantial work over the last decade on the representation theory of restricted Lie algebras of classical type. While some of this work has been associated with the solution of the classification problem, much more of it has been motivated by connections with the modular representation theory of semisimple algebraic groups. Finally, the study of the representation theory of affine Lie algebras has been one of the most rapidly growing parts of algebra since its inception twenty years ago. The problem of finding explicit constructions of modules for affine Lie algebras has been attacked by various methods. This project will support the Conference on Structure and Representation of Lie Algebras to be held from April 17-19, 1992 at Yale University. Topics will include the classification and structure of finite dimensional Lie algebras, representation theory of finite dimensional Lie algebras over fields of positive characteristics, and representation theory of Kac-Moody Lie algebras. The format will consist of plenary lectures of an expository nature by leading experts as well as some shorter, more specialized talks.

李代数理论在本世纪的数学研究中发挥了重要作用。有限维半单李代数、模李代数和Kac-Moody李代数都扮演着重要的角色。在有限维李代数的分类和结构方面最引人注目的进展是最近解决了特征为P0的代数闭域上的单李代数的分类问题。尽管有这些工作，许多重要的研究领域仍然存在，包括利用同调性质刻画重要的李代数类(例如，幂零的，可解的)，以及寻找结构结果。在过去的十年里，在经典类型的限制李代数的表示理论方面也有大量的工作。虽然其中一些工作与分类问题的解决有关，但更多的工作是由于与半单代数群的模表示理论的联系而进行的。最后，自二十年前仿射李代数诞生以来，对它的表示理论的研究一直是代数中发展最快的部分之一。仿射李代数模的显式构造问题已被各种方法所攻克。该项目将支持1992年4月17日至19日在耶鲁大学举行的李代数结构和表示会议。主题包括有限维李代数的分类和结构，正特征域上的有限维李代数的表示理论，以及Kac-Moody李代数的表示理论。其形式将包括主要专家的说明性全体演讲以及一些较短、更专门的演讲。