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

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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.