Lie Groups and Lie Algebras
(dt. Lie-Gruppen und Lie-Algebren)
|Level, degree of commitment in original study programme||Intermediate module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Mathematics.|
|Original study programme||B.Sc. Mathematik / Mathematik Wahlpflichtmodule|
|One semester, |
Regelmäßig im Wechsel mit den anderen intermediate moduleen
|Person in charge of the module's outline||Prof. Dr. Ilka Agricola, Prof. Dr. István Heckenberger, Prof. Dr. Pablo Ramacher|
- 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.
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.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis. Basic knowledge of algebra is advantageous, but not mandatory.
- 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
This page describes a module according to the latest valid module guide in Wintersemester 2022/23. 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:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
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.