Lie Groups (GeomLie)

Course content

(A) Lie groups and Lie algebras; definitions and examples.
(B) Invariant vector fields and the exponential map.
(C) The Lie algebra of a Lie group, Ad and ad.
(D) Homomorphisms, subgroups, sub¬algebras.
(E) Fibre bundles and homogeneous spaces.
(F) Representations of sl(2,C)
(G) Examples of representations of other groups; compact groups.


MSc Programme in Mathematics

Learning outcome

Knowledge: basic definitions, examples and theorems of the theory
Skill: ability to use the above
Competence: perform logic reasoning within the theory

5 hours of lectures and 2 hours of exercises per week for 9 weeks.

Geometri 2 (Geom2) or similar.

7,5 ECTS
Type of assessment
Continuous assessment
3 mandatory homework assignments to be returned in weeks 5, 7 and 9 of the course. The assignments counts 30%, 30%, and 40%, respectively.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 45
  • Theory exercises
  • 18
  • Preparation
  • 143
  • English
  • 206