Universität Wien

250307 VO Lie algebras and representation theory (2008S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 05.03. 10:00 - 12:00 Seminarraum
  • Thursday 06.03. 10:00 - 12:00 Seminarraum
  • Wednesday 12.03. 10:00 - 12:00 Seminarraum
  • Thursday 13.03. 10:00 - 12:00 Seminarraum
  • Wednesday 19.03. 10:00 - 12:00 Seminarraum
  • Thursday 20.03. 10:00 - 12:00 Seminarraum
  • Wednesday 26.03. 10:00 - 12:00 Seminarraum
  • Thursday 27.03. 10:00 - 12:00 Seminarraum
  • Wednesday 02.04. 10:00 - 12:00 Seminarraum
  • Thursday 03.04. 10:00 - 12:00 Seminarraum
  • Wednesday 09.04. 10:00 - 12:00 Seminarraum
  • Thursday 10.04. 10:00 - 12:00 Seminarraum
  • Wednesday 16.04. 10:00 - 12:00 Seminarraum
  • Thursday 17.04. 10:00 - 12:00 Seminarraum
  • Wednesday 23.04. 10:00 - 12:00 Seminarraum
  • Thursday 24.04. 10:00 - 12:00 Seminarraum
  • Wednesday 30.04. 10:00 - 12:00 Seminarraum
  • Wednesday 07.05. 10:00 - 12:00 Seminarraum
  • Thursday 08.05. 10:00 - 12:00 Seminarraum
  • Wednesday 14.05. 10:00 - 12:00 Seminarraum
  • Thursday 15.05. 10:00 - 12:00 Seminarraum
  • Wednesday 21.05. 10:00 - 12:00 Seminarraum
  • Wednesday 28.05. 10:00 - 12:00 Seminarraum
  • Thursday 29.05. 10:00 - 12:00 Seminarraum
  • Wednesday 04.06. 10:00 - 12:00 Seminarraum
  • Thursday 05.06. 10:00 - 12:00 Seminarraum
  • Wednesday 11.06. 10:00 - 12:00 Seminarraum
  • Thursday 12.06. 10:00 - 12:00 Seminarraum
  • Wednesday 18.06. 10:00 - 12:00 Seminarraum
  • Thursday 19.06. 10:00 - 12:00 Seminarraum
  • Wednesday 25.06. 10:00 - 12:00 Seminarraum
  • Thursday 26.06. 10:00 - 12:00 Seminarraum

Information

Aims, contents and method of the course

The first part of this lecture introduces the elementary concepts and the basic definitions: Lie algebras, representations, derivations, Lie groups. Then we discuss abelian, nilpotent and solvable Lie algebras. We prove the theorems of Engel and Lie, and the solvability criterion of Cartan. Then simple, semisimple and reductive Lie algebras are discussed. Further topics are the classification of simple complex Lie algebras, the theorem of Weyl, the theorems of Levi and Malcev and the Cartan criterion for semisimple Lie algebras.
We classify simple representations of complex semisimple Lie algebras.

Assessment and permitted materials

Minimum requirements and assessment criteria

The aim of this lecture is to provide the basic theory and knowledge on Lie algebras and representation theory, as it is necessary for further directions of Differential
Geometry and Number Theory. To be more precise, we list a few of the directions: Lie Groups, Geometric structures on manifolds, Crystallographic groups, Arithmetic of Algebraic Groups, Automorphic Forms and L-functions, Real and p-adic Lie Groups,
Geometry of Arithmetic Varieties and other directions.

Examination topics

Reading list

1.) Jacobson, Nathan: Lie algebras. 1962
2.) Serre, Jean-Pierre: Lie algebras and Lie groups. 1965
3.) Stewart, I.: Lie algebras. 1970
4.) Winter, David J.: Abstract Lie algebras. 1972
5.) Humphreys, J.E.: Introduction to Lie algebras and representation theory. 1972
6.) Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. 1974
7.) Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
8.) Bahturin, Ju.A.: Lectures on Lie algebras. 1978
9.) Onishchik, A.L.: Introduction to the theory of Lie groups and Lie algebras. 1979
10.) Zassenhaus, Hans: Lie groups, Lie algebras and representation theory. 1981
11.) Postnikov, M.M.: Lie groups and Lie algebras. 1982
12.) Kirillov, A.A.: Representations of Lie groups and Lie algebras. 1985
13.) Seligman, George B.: Constructions of Lie algebras and their modules. 1988
14.) Knapp, Anthony W.: Lie groups, Lie algebras, and cohomology. 1988
15.) Hilgert, Joachim; Neeb, Karl-Hermann: Lie-Gruppen und Lie-Algebren. 1991
16.) Carter, Roger: Lie algebras of finite and affine type. 2005

Association in the course directory

MALV, MGEV

Last modified: Mo 07.09.2020 15:40