Introduction to Lie Algebras

Course content

1) Lie algebras

2) Matrix Lie algebras

3) Some representation theory

4) Structure theory of Lie algebras

5) Cartan-Weyl basis

6) Classification of simple Lie algebras


MSc Programme in Mathematics

Learning outcome

At the end of the course the students are expected to have acquired the following knowledge and associated tool box:

  • the mathematical framework of Lie algebras, including basic examples in the form of matrix Lie algebras 
  • basic representation theory of Lie algebras
  • structure theory of Lie algebras, with main emphasis on semi-simple Lie algebras
  • Killing form, roots, and root space decomposition
  • the fundamental classification theorems for simple Lie algebras, including Serre's theorem 



  • be able to use the fundamental results on Lie algebras to solve concrete mathematical problems
  • be able to work rigorously with representaions of Lie algebras, including decompositions in special cases 
  • be able to formulate and solve certain types of physical problems by applying the theory of Lie algebras and their representations


Competences: The course aims at training the students in formulating and handling specific mathematical problems, possibly inspired by physics, by use of the theory of Lie algebras and their representations.

8 weeks with 2x2 lectures and 2x2 exercise sessions per week.

Lecture notes will be made available through Absalon.

Knowledge of linear algebra, e.g., the course LinAlg.

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Two longer written assignments in week 5 and week 9, plus 5 smaller written assignments in weeks 2,3,4,6,7. The assignments will be graded on a scale from 0 to 100% and in order to pass the student must obtain at least 50% for each assignment.
All aids allowed
Marking scale
passed/not passed
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
  • 32
  • Theory exercises
  • 32
  • Preparation
  • 122
  • Exam
  • 20
  • English
  • 206