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Representation Theory of Lie Algebras
Darstellungstheorie von Lie-Algebren
Last Updated: 2026-02-05 15:14:49
Abstract
Definition of Lie algebras, Properties. Theorems of Engel, Lie. Weyls Theorem. Representation theory of sl_2. Root systems, root space decomposition. Classification of Lie simple algebras. Dynkin diagrams. PBW theorem. Generators and Relations. Representation theory of Lie algebras. Weights. Highest weight modules: Existence and Uniqueness. Examples (sl_3).
Objective
Definition of Lie algebras, Properties, Examples. Theorems of Engel, Lie. Representations of semi-simple Lie algebras are completely reducible (Theorem of Weyl). Classification of irreducible representations of sl_2. Weights. Root systems, root space decomposition. Classification of Lie simple algebras. Dynkin diagrams. Universal enveloping algebra, PBW theorem. Generators and Relations of a semi-simple Lie algebra. Representation theory of semi-simple Lie algebras. Weights, weight lattice. Highest weight modules: Existence and Uniqueness. Examples (representations of sl_3).
General Information
- Language
- German
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Darstellungstheorie von Lie-Algebren |
|
2 h weekly |