Math 7370, Lie Groups and Representation Theory

Time and location: 3:00 to 4:20, T-Th 284 Lockett

Book: We will not be using any book, only my own lecture notes. But you can find some information on good book bellow.


INSTRUCTOR Gestur Olafsson
Office 322 Lockett
Office Hours Tuesday, Wednesday and Thursday at 12:30-1:30 pm, and by request. Please email me in case you would like to meet outside the office hours
Phone 578-1608 and 225-337-2206 (cell)
e-mail olafsson"at"math"dot"lsu"dot"edu
Homework problem section There will be some homework during the semester a midterm exam and a final exam. See below for more information.
Grader To be announced later.

Important Dates:

  1. Monday, August 26: Classes starts. Our first meeting is on Tuesday, August 27.
  2. Monday, September 2: Labour day, no classes.
  3. Tuesday, October 15: Midterm exam in class.
  4. Tuesday, November 7: Fall break starts
  5. Wednesday, November 27: Thanksgiving holidays begins 12:30 pm.
  6. Wednesday, December 4: Concentrated Study Period starts. Classes ends Sat. Dec. 7.
  7. Thursday, December 12, 5:30-7:30: Final exam. The exam will take place in 038 Allen Lockett


Real analysis Math 7311. Basic differential geometry is also helpfull. Please contact me if you need more information.

Assignments, Tests, and Grades

Problems, mainly proofs, will be assigned frequently, approximately every second week. I will only randomly correct the homework. But, we will have a optional problem section every second week. Here we will discuss the homework and questions related to the class. We will decide on the time for the problem section during the second week of class. There will be three homework sets that I will grade. Only those homeworks will count towards the final grade.

There will be a Mid-term Exam and a Final Exam. These tests may include any question (or variation thereupon) in a covered section of the text. More than half of the questions will be based on the homeworks. Some of the questions will includes proofs.

Grades: The homework will count for 30% of the final grade, the midterm 30% and the final will be 40%.

The Scale is: 90 -100 (A), 80-89 (B), 70-79 (C), 60-69 (D), Below 60 (F).

Material Covered in Class

  1. Definition of Lie groups and their Lie algebra..
  2. Proof of the theorem that a closed subgroup of a Lie group is a Lie group.
  3. Examples of Lie groups.
  4. Matrix Lie groups and the exponential map.
  5. Group actions, basic representation theory and homogeneous spaces.
  6. Proof of the theorem: If G is a matrix group and H is a closed subgroup of G then G/H is a manifold and G acts smoothly.
  7. Homogeneous vector bundles
  8. Lie algebras: Nilpotent, solvable, semisimple, reductive.
  9. Every compact Lie group is reductive
  10. If there is time: Some overview of the classification of simple Lie algebras.


We will not use any fixed book. But there are some good books around; Here is a short list:

  • J. Hilgert and K-H. Neeb: "Structure and Geometry of Lie Groups", Springer. This book is close to the material of the course, but quite big.
  • V.S. Varadarajan: "Lie Groups, Lie Algebras, and Their Representations". Springer. A classic textbook. You can find everything we do (and more) in here.
  • AMS has also a nice little booklet: A. Arvanitoyeorgos: "An Introduction to Lie Groups and Geometry of Homogeneous spaces"