Course teacher(s)
Simone GUTT (Coordinator)ECTS credits
5
Language(s) of instruction
french
Course content
Lie groups: definition, examples, the Lie algebra of a Lie group, Lie subgroups, correpondance with Lie subalgebras, the exponential map, Campbell-Baker- Hausdorf formula, homogeneous spaces. Lie algebras : nilpotent algebras and Engel's theorem, solvable algebras and Lie's theorem, semisimple Lie algebras, Killing form, Cartan's criteria, Chevalley cohomology, Weyl's theorem, Levu's decomposition, Ado's theorem... Classification of simple complex Lie algebras.
Objectives (and/or specific learning outcomes)
Goal : Introduce the structures of Lie groups and Lie algebras.
Prerequisites and Corequisites
Cours co-requis
Teaching methods and learning activities
Teaching Method : ex-cathedra course with exercices suggested to illustrate the notions.
Other information
Contacts
Simone Gutt 2.O.7.116 Email sgutt@ulb.ac.be
Evaluation
Method(s) of evaluation
- Other
Other
Assessment : oral exam. The students prepare and present a topic in front of the class and are asked about general facts from the course.