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 be offered this semester (Fall 2017). It is instructed by V. G. Kac.

Lecture occurs 2:30 PM to 4:00 PM on Tuesdays and Thursdays in 2-139.

This class counts for a total of 12 credits.

You can find more information at the 18.745 Course Description (Spring 2015) site or on the 18.745 Stellar site.

MIT 18.745 Introduction to Lie Algebras Related Textbooks
MIT 18.745 Introduction to Lie Algebras On The Web
18.745 Course Description (Spring 2015)
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helgason algebra problem alexander kirillov lie algebras cartan

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