# Fiches de cours

## Lie groups

#### Enseignant(s) :

Urech Christian Lucius

English

#### Summary

Lie groups are manifolds with a group structure. The interaction between the geometric and the algebraic structure of these objects gives rise to a rich and beautiful subject with various applications in physics and other branches of mathematics.

#### Content

- Lie groups and Lie algebras
- Classical groups
- The exponential map
- Lie subgroups and Lie subalgebras
- Homomorphisms between Lie groups
- Decomposition theorems

#### Keywords

Lie groups, Lie algebras, Classical groups

#### Learning Prerequisites

Group Theory

##### Recommended courses

Introduction to differentiable manifolds

Lie algebras

#### Learning Outcomes

By the end of the course, the student must be able to:
• Define the main concepts introduced in the course
• state the theorems covered in the course and give the main ideas of their proofs
• apply the results covered in the course to examples
• deduce properties of a Lie group from the structure of its Lie algebra

#### Teaching methods

ex-cathedra teaching, exercise classes

#### Expected student activities

Attending the course, solving the weekly assignments, participating actively in the exercise classes

#### Assessment methods

Assignments, oral exam

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

### Dans les plans d'études

• Mathématiques - master, 2019-2020, Master semestre 2
• Semestre
Printemps
• Forme de l'examen
Oral
• Crédits
5
• Matière examinée
Lie groups
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Ingénierie mathématique, 2019-2020, Master semestre 2
• Semestre
Printemps
• Forme de l'examen
Oral
• Crédits
5
• Matière examinée
Lie groups
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Ingénierie mathématique, 2019-2020, Master semestre 4
• Semestre
Printemps
• Forme de l'examen
Oral
• Crédits
5
• Matière examinée
Lie groups
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction
Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand