Locally compact groups
| Fact sheet | |
|---|---|
| Faculty: |
Faculty 07 - Mathematics and Computer Science, Physics, Geography |
| Department: | Department of Mathematics |
| Title: | Locally compact groups |
| Code: | 0703 |
| Lecturer: | Prof. Dr. Ralf Köhl |
| Type of course: | Reading course |
| Description: | Matrix groups like GL(n,R) carry a group structure and inherit a topology as a subspace of the vector space of all n-by-n square matrices. Continuity of matrix multiplication and of the determinant plus Cramer’s matrix inversion rule actually allow one to make this group an example of a topological group. Moreover, it can be endowed with the structure of a differentiable manifold, making it a so-called (linear) Lie group. One key feature is the fact that its natural topology inherited from the space of n-by-n square matrices is a locally compact topology, allowing one to introduce the so-called Haar measure and Haar integral. This course will be based on the book “Locally compact groups” by Markus Stroppel. We will cover Topological Groups, Topological Transformation Groups, and the Haar Integral in considerable detail, with an application to the theory of linear representations and glimpses to further topics. This course is very well suited as a preparatory course for a BSc Thesis on topological groups and as a first introduction towards specializing in geometry & topology / group theory / representation theory during an MSc curriculum. |
| Date/Time: |
Asynchronous / weekly tasks |
| Language: | English |
| Target group: | BSc Mathematics in their third year / MSc Mathematics / BSc Physics in their third year / Msc Physics |
| Requirements for participation: | Knowledge in Linear Algebra, Algebra, Analysis (optional: measure theory) |
| ECTS: | 6 |