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MATH-F417

Groupes et algèbres de Lie

academic year
2024-2025

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.

Programmes