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Semisimple Lie Algebras
Halbeinfache Lie-Algebren
Last Updated: 2026-02-05 16:37:25
Abstract
In this lecture, we study the theory of complex semisimple Lie algebras.
Objective
The classification of complex semisimple Lie algebras and their finite-dimensional representation.
Content
-Brief introduction to the general theory of Lie algebras -Root systems and root space decompositions of semisimple Lie algebras -Dynkin diagrams and the classification of semisimple Lie algebras -Representation theory of semisimple Lie algebras
Resources
Lecture Notes
R. Suter, "Lie-Algebren und ihre Darstellungen", Skript,https://imsc.uni-graz.at/baur/lehre/WS2012-LieAlg/Skript-Lie-Suter.pdf
Literature
-J.E. Humphreys, "Introduction to Lie Algebras and Representation Theory", Springer-Verlag New York Inc., 1972 -J.-P. Serre, "Complex semisimple Lie algebras", Springer-Verlag New York Inc., 1987 -B.C. Hall, "Lie Groups, Lie Algebras, and Representations: An Elementary Introduction", Springer-Verlag New York Inc., 2003
General Information
- Language
- German
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Halbeinfache Lie-Algebren |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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