18.745 Introduction to Lie Algebras


Class Info

Topics may include structure of finite-dimensional Lie algebras; theorems of Engel and Lie; Cartan subalgebras and regular elements; trace form and Cartan's criterion; Chevalley's conjugacy theorem; classification and construction of semisimple Lie algebras; Weyl group; universal enveloping algebra and the Casimir operator; Weyl's complete reducibility theorem, Levi and Maltsev theorems; Verma modules; classification of irreducible finite-dimensional representations of semisimple Lie algebras; Weyl's character and dimension formulas.

This class has 18.701, and 18.703 as prerequisites.

18.745 will not be offered this semester. It will be available in the Spring semester, and will be instructed by G. Lusztig.

This class counts for a total of 12 credits. This is a graduate-level class.

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