*Instructor:* Dr. Szilárd SZABÓ

*Text:* Wulf Rossmann:
Lie Groups: An Introduction through Linear Groups, Oxford Graduate Texts in Mathematics 5.

*Prerequisite:*
Although the general theory of Lie groups heavily relies on topics such as for instance the notion of a differentiable manifold, we choose a path into the topic that assumes familiarity only with elementary linear algebra, the basics of group theory and multivariable calculus. The few concepts of point-set topology that are needed will be developed in a way that's tailor-suited to the purposes of the course. The idea behind this choice is that the classical examples should motivate and make more accessible the general definitions and results.

*Topics:*

- Vector fields and one-parameter groups of matrices
- The properties of the exponential map
- The Campbell--Baker--Hausdorff formula
- Linear groups
- The Lie-algebra of a linear group
- Coordinates on a linear group
- Connected groups
- The Lie correspondence
- Homomorphisms of linear groups
- Closed subgroups of linear groups
- The classical matrix groups
- Cartan subgroups, the Weyl group
- Roots, weights and reflections
- Lie groups and algebras