Course on Lie groups: general theory, January - February 2001

Lecturer: T.H. Koornwinder

Location and time:
room P015A, Tuesday 11.15-13.00 hour and Wednesday 13.15-16.00 hour.
The last hour on Wednesday (15.15-16.00 hour) is an exercise class.

First session: Tuesday January 9, 11.15-13.00 hour

Last session: Wednesday February 7, 13.15-16.00 hour

Exam:
Submit at least one exercise per week. Furthermore an oral examen about part of the theory. Instead of an oral examen, it can be convened that you write a short paper about some topic related to the theory.

Course material:
Lecture notes will be provided. Part of these notes will closely follow Chapters 1,2,5 in G. Segal's lecture notes on Lie groups, which form the middle part of the book:
R. Carter, G. Segal and I. Macdonald, Lectures on Lie groups and Lie algebras, London Mathematical Society Student Texts 32, Cambridge University Press, 1995.

Syllabus

• Ch. 1. Generalities about topological groups (pp. 1-4)
• Ch.2. SU(2), SO(3) and SL(2,R) (pp. 1-9)
• Ch.3. Differentiable manifolds (pp. 1-8)
• Ch.4. The exponential mapping (pp. 1-5)
• Ch.5 The Lie algebra of an abstract Lie group (pp. 1-8)
• Ch.6 The Lie algebra of an abstract Lie group (pp. 1-6)