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German original

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,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben.
Prüfungsleistung: Klausur oder mündliche Prüfung
Language,
Grading
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
Duration,
frequency
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

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.


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 Wintersemester 2018/19. 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.