Lie Groups - M1 - 8EC

Prerequisites
Basic knowledge of linear algebra, analysis, topology, group theory and differential geometry.
It is recommended that the student has already followed (at least) one course on each of these
subjects.

From topology: open/closed sets, continuity, compactness, connnectedness, metric spaces,
Hausdorff, local compactness.

The following notions from differential geometry will appear in the course: smooth manifolds,
submanifolds, smooth maps, tangent spaces, vector fields, flow/integral curves of vector fields,
differential forms, integration with differential forms, immersions and submersions.
The more advanced of these can be learned during the course or treated as a black box, but
familiarity with the basic parts is indispensible.

Aim of the course
The aim of this course is to give a thorough introduction to the theory of Lie groups.
Topics that will be covered include:
- general properties of Lie groups (subgroups, homomorphisms, quotients),
- the Lie algebra of a Lie group, and the exponential map,
- continuous group actions and invariant integration,
- harmonic analysis on compact Lie groups, up to the Peter-Weyl theorem.

Lecturers
Erik Koelink and Walter van Suijlekom (Radboud Universiteit Nijmegen)

Assistant: Kevin Zwart (Radboud Universiteit Nijmegen)

Homework

During the semester there will be four homework assignments (so not every week). Together, these will count for 30% of the final grade, also in the case of a retake.

Exam and retake

These will be in written form. The exam (or retake) counts for 70% of the final grade. In addition, to pass the course a student has to score at least 5.0 for the exam (or retake).

Lecture notes & Literature:

"Lie groups" by E. van den Ban, and additional notes by M. Solleveld.
These will be made available on the mastermath website.
For those who prefer a book, "Lie groups" by Duistermaat and Kolk is recommended.

If you want to refresh or extend your knowledge of smooth manifolds: chapter 1 of "Foundations of differentiable manifolds and Lie groups" by Warner contains useful material.