Theory and Applications of Simple Lie-Algebras

Module PH2136

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2136 is a semester module in German or English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 40 h 5 CP

Responsible coordinator of the module PH2136 is Norbert Kaiser.

Content, Learning Outcome and Preconditions


definition and basic notions for Lie algebras, low-dimensional examples, representations of sl(2,C), classical Lie algebra, root space decomposition of semi-simple Lie algebras, root systems and their complete classification through Dynkin diagrams, exceptional Lie algebras, representations and fundamental dominant weights, real and coplex Clifford algebras and their complete classification  

Learning Outcome

The student knows the basic notions of Lie algebras and the differences between real and complex Lie algebras.The The student knows the basic that semi-simple Lie algebras possess a root space decomposition and that the corresponding root systems can be completely classified.

The student knows that representations of semi-simple Lie algebras are determined by highest weights and that these a integral linear combinations of fundamental dominant weights.

The student knows the generalization of the Dirac algebra in form of the complete classification of the real and complex Clifford algebras.


linear algebra

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Theorie und Anwendung einfacher Lie-Algebren Kaiser, N. Mittwoch, 14:00–16:00

Learning and Teaching Methods

no info


no info


no info

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.