1) 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.
2) 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.
3) Rules about Homework/Exam
Homework: During the semester there will be biweekly homework assignments (so not every week). Together, these will count for at most 30% of the final grade, also in the case of a retake.
Exams: These will be in written form. In order to pass the course a student has to score at least 5.0 for the exam (or retake). The final grade is the maximum of the exam and the average of exam (70%) and
homework (30%). The grade for the homework is the average of the best 5 results (out of 7) and has to be at least 6.0 in order to count for the final grade.
4) Lecture notes/Literature
The course will be based on an extensive studyguide, which contains precise references to primary and secondary literature. This studyguide will be made available via ELO.
- Docent: Erik Koelink
- Docent: Walter van Suijlekom