This page contains some information that can be helpful before you register for the course. After registration, we will use ODTUclass. You should follow ODTUclass and check your emails regularly for important announcements during the semester.
Course Objectives
Lie groups and Lie algebras are especially important in the study of group actions on vector spaces. Besides explaining problems in several areas in mathematics, Lie algebras are interesting in their own right. The classification of simple complex Lie algebras is a beautiful application of linear algebra. The aim of this course is to introduce some of the techniques for studying Lie algebras.
Lectures Hours
The first meeting is on Wednesday, September 23 at ??:?? in ????. The lecture hours will be decided during this meeting.
Grading
There will be two midterm exams and a final exam. The time and the method of each exam will be announced later.
- Midterm 1, 30 points – around the 6th week.
- Midterm 2, 30 points – around the 11th week.
- Final, 40 points – during the final exam period.
Textbooks and Tentative Course Outline
- K. Erdmann, M. J. Wildon, Introduction to Lie Algebras. In the first part, we will cover the basic structure theory of complex semi-simple Lie algebras including the classification by root systems and Dynkin diagrams.
- B. Hall, Lie Groups, Lie Algebras, and Representations. An Elementary Introduction, Second Edition. In the second part, we wil cover the basic representation theory of Lie groups starting with elementary properties and going through the standard results up to Weyl character formula.
Course Readings
- William Fulton, Joe Harris, Representation theory: a first course.
- J. E. Humphreys, Introduction to Lie Algebras and Representation Theory.
- N. Bourbaki, Lie Algebras and Lie Groups.
PARI/GP
The software PARI/GP is very simple to learn and extremely strong to do computations with.