- Review of differentiable manifolds, definition of a Lie group. Quotients in the category of Lie groups, homogeneous manifolds, haar measure, connected components.
- Algebraic groups, matrix groups, the classical groups.
- Lie algebras and connection to Lie groups.
- Nilpotent, solvable and semisimple Lie algebras and Lie groups, Lie theorem, Engel theorem, Levi decomposition.
- Cartan-Killing form.
- Representation of a Lie algebra over the complex numbers.
- Root and weights, root systems, Dynkin diagrams, classication of complex semisimple Lie algebras.
University course catalogue: 201.2.4141