# 18.755 Introduction to Lie Groups

• Meeting time: Tuesday/Thursday 2:30-4:00, Room 2-143
• Text: Alexander Kirillov, Jr., An Introduction to Lie Groups and Lie Algebras.
• A beautiful older text explaining perfectly the dictionary between Lie groups and Lie algebras is Frank Warner's Foundations of differentiable manifolds and Lie groups. An elegant treatment of the structure theory for Lie algebras is James Humphreys' Introduction to Lie algebras and representation theory.

David Vogan, 2-355

dav@math.mit.edu

Telephone x3-4991

Office hours Monday 3:00-5:00, Friday 12:00-1:00 (or any time).

Problem sets will be posted here. Approximate plan is that problems assigned in class each week will be due in class the following Tuesday. Usually I hope to post solutions immediately after class Tuesday. This means that problem sets must be submitted either in class, or to my office before class. (Electronic submissions before class are OK.) No extensions and no exceptions. The grading for the course will emphasize your best work, so missing one problem set should not have a serious effect.

First problem set due in class Tuesday, September 12.
First problem set solutions, to be posted after class 9/12.

Second problem set due in class Tuesday, September 19. The original version used the letter n to mean two different things in the first problem, so that the statement didn't make sense. The version now linked fixes that.
Second problem set solutions, to be posted after class 9/19.

Third problem set due Tuesday, September 26. The "C" version now linked corrects a minor typo in problem 2, and the due date (thank you to Yang Liu and Zhengjiang Lin for reading carefully!)
Third problem set solutions, to be posted after class 9/26.

Fourth problem set due Tuesday, October 3.
Fourth problem set solutions.

Fifth problem set due Thursday, October 12.
Fifth problem set solutions, to be posted after class 10/12.

Sixth problem set due Tuesday, October 17.
Sixth problem set solutions, to be posted after class 10/17.

Seventh problem set due Tuesday, October 24. The version B now linked corrects a typo in the definition of M_\xi (thank you, Nat!)
Seventh problem set solutions, to be posted after class 10/24.

Eighth problem set due Tuesday, October 31.
Eighth problem set solutions, to be posted after class 10/31.

Ninth problem set due Tuesday, November 7.
Ninth problem set solutions, to be posted after class 11/7.

Tenth problem set due Tuesday, November 14.
Tenth problem set solutions, to be posted after class 11/14. (The solutions initially posted were accidentally an incomplete draft. Actual solutions have a "D" in the file name, and were posted 11:15 pm Tuesday. Thank you Nat for pointing this out!)

Eleventh problem set due Tuesday, November 21.
Eleventh problem set solutions, to be posted after class 11/21.

Twelfth problem set due Tuesday, December 5. What is now linked corrects an error in the original version: it was necessary to replace "2m" by "n" twice in the formulation of Problem 1.

Twelfth problem set solutions, to be posted after class 12/5.

Relevant to class around 10/30 and to Problem Set 10 is notes on Weyl and Clifford algebras. I will be very grateful for corrections or suggestions about improvements.

Here is a set of notes on root systems, related to Chapter 7 of the text. This provides additional details on material I'll discuss in class December 5, 7, and 12.

The notes that follow are older and not (so far) related to the 2015 course. Here are notes on compact classical groups.

Notes about actions of a Lie group on a manifold. You should also remember that the group SL(2,R) by its definition acts on the two-dimensional vector space R^2. Is there a way to get out of that an action on a circle?

Notes about quaternionic matrix groups. Goal is to relate quaternionic groups to complex groups. Edited Wednesday afternoon 11/5/14 to remove almost all coordinates.