18.745 Introduction to Lie Algebras
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.
18.745 will be offered this semester (Fall 2018). It is instructed by V. G. Kac.
Lecture occurs 2:30 PM to 4:00 PM on Tuesdays and Thursdays in 2-143.
This class counts for a total of 12 credits.
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