Lie groups

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.

Content

Keywords

Lie groups, Lie algebras, Classical groups

Learning Prerequisites

Required courses

MATH-211

Recommended courses

MATH-302

MATH-303

MATH-322

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

Resources

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

Ressources en bibliothèque

• Introduction to Smooth Manifolds / Lee
• Lie groups, beyond an introduction / Knapp
• Lie Groups / Bump
• Introduction to the Theory of Lie Groups / Godement
• Matrix Groups / Baker

Moodle Link

• https://go.epfl.ch/MATH-429