Introduction to Lie groups and Lie algebras

Course description: This is an introduction to the theory of Lie groups, Lie algebras, and their representations. The course is intended for graduate students in mathematics and physics with little or no prior exposure to the Lie theory. We will focus on matrix Lie groups and Lie algebras to keep the exposition concrete. First we will look at the relationship between Lie groups and Lie algebras, along with basic representation theory. One of the main objects is the exponential map, and we will study its properties including the Baker-Campbell-Dynkin-Hausdorff formula. Then we will study root systems, and classification of semisimple Lie algebras. We will also look at how the Lie theory is used in applications such as differential geometry (e.g. symmetric spaces) and physics. The only prerquisite for taking the course is a background in linear algebra.

Lecture times:  Tuesday, Thursday   12:30-1:45 PM.

Lecture place:  MSB 215.  

Instructor:  Masha Gordina,   MSB 304.

Office hours: by appointment.

Textbook: Suggested textbook: Lie Groups, Lie Algebras, and Representations by Brian C. Hall, Springer.

Homework: There will be homework assigned during lectures and posted on the course home page.