MATH-429 / 5 crédits

Enseignant: Michel Philippe

Langue: Anglais

## Summary

We will discuss the basic structure of Lie groups and of their associated Lie algebras along with their finite dimensional representations and with a special emphasis on matrix Lie groups.

## Keywords

Lie groups, Lie algebras, Classical groups

MATH-211

MATH-302

MATH-303

MATH-322

MATH-319

## 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

• Participation to the course the course
• Active participation to the exercise sessions and to the resolution of exercises

## Assessment methods

Assignments, oral exam

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

## Supervision

 Office hours No Assistants Yes Forum No

## Bibliography

"Introduction to Smooth Manifolds", John M. Lee

"Introduction to the Theory of Lie Groups", Roger Godement

"Matrix Groups: An Introdudion to Lie Group Theory", Andrew Baker

"Lie Groups", Daniel Bump

"Lie groups, beyond an introduction", Anthony Knapp

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Lie groups
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Lie groups
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Lie groups
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 MAA330 9-10 10-11 MAA330 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mercredi, 8h - 10h: Cours MAA330

Mercredi, 10h - 12h: Exercice, TP MAA330

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