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 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