Coursebooks

Lie groups

MATH-429

Lecturer(s) :

Urech Christian Lucius

Language:

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

Required courses

Group Theory

Recommended courses

Introduction to differentiable manifolds

Lie algebras

Learning Outcomes

By the end of the course, the student must be able to:

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.

In the programs

  • Mathematics - master program, 2019-2020, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Lie groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2019-2020, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Lie groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2019-2020, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Lie groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German