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.


  1. Vector fields and one-parameter groups of matrices
  2. The properties of the exponential map
  3. The Campbell--Baker--Hausdorff formula
  4. Linear groups
  5. The Lie-algebra of a linear group
  6. Coordinates on a linear group
  7. Connected groups
  8. The Lie correspondence
  9. Homomorphisms of linear groups
  10. Closed subgroups of linear groups
  11. The classical matrix groups
  12. Cartan subgroups, the Weyl group
  13. Roots, weights and reflections
  14. Lie groups and algebras