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

李代数的理论在 数学研究在这个世纪。 重要角色有 被有限维半单李代数玩过， 模李代数和Kac-Moody李代数。 最 在有限的分类和结构方面取得了巨大的进展 维李代数一直是最近的解决方案， 代数上单李代数的分类问题 闭域特征p0。 尽管如此，许多 重要的研究领域仍然存在，包括 李代数的重要类的特征化（例如， 幂零，可解）的同调性质和搜索 结构结果。 此外，还进行了大量工作， 限制性李的表示论 古典型代数 虽然其中一些工作 与分类问题的解决有关， 更多的动机是与模块化的联系 半单代数群的表示理论 最后， 仿射李代数表示论的研究 是代数中发展最快的部分之一， 20年前成立。 寻找显式的 仿射李代数的模的构造一直是 被各种方法攻击。 该项目将支持结构问题会议， 李代数的表示将于1992年4月17-19日举行 在耶鲁大学。 主题将包括分类和 有限维李代数的结构，表示 正域上有限维李代数理论 特征和表示理论 代数 该格式将包括全体讲座的一个 由领先的专家以及一些较短的， 更专业的谈话。

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.