Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups.
The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it.
Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester.
The exercise sheets will be posted here.
| Exercise Sheet | Solution | Comment |
|---|
The lecture will start on Thursday, 21st of September 2017.
Every second week there will be an exercise class led by Yannick Krifka instead of a lecture on Thursday.
| time | room |
|---|---|
| Tue 10-12 am | HG D 5.2 |
| Thu 08-10 am | HG D 3.2 |
