Main content

This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.

Lie Groups and Lie Algebras
(dt. Lie-Gruppen und Lie-Algebren)

Level, degree of commitment Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Written or oral examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with the other advanced modules
Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. István Heckenberger, Prof. Dr. Pablo Ramacher

Contents

  • Basic notions on Lie groups and Lie algebras: Relationship between Lie groups and Lie algebras, exponential function, rough classification of Lie algebras, fundamental theorems (Engel, Lie, Cartan...).
  • Structure theory of simple Lie algebras: Cartan subalgebras, roots, Weyl group, universal enveloping algebra.
  • Representation theory: Fundamentals of finite-dimensional theory, highest weights, Weyl chambers, possibly Verma modules.

Qualification Goals

The students shall

  • learn the algebraization of a fundamental concept of symmetry,
  • learn about the interaction of geometric and algebraic methods,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction and formulating proofs),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden. Grundkenntnisse in Algebra und Analysis 3 sind vorteilhaft, aber nicht zwingend


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Computer Science
  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.


Recommended Reading

  • Fulton-Harris, Introduction to representation theory, Springer
  • Bröcker- tom Dieck, Representations of Compact Lie Groups, Springer
  • Goodman-Wallach, Representations and invariants of the classical groups, Cambridge University Press



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2016/17. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.