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401-3172-57L 4 Credits BSC , MSC D-PHYS , D-MATH

Representation Theory of Lie Algebras

Darstellungstheorie von Lie-Algebren

Lecturers & Examiners: Prof. Dr. Karin Ursula Baur
VVZ CR n/a

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
  • Mon 08:15-10:00 (HG E 33.5)
2 h weekly

Offered In