Universität Wien
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250309 VO Lie algebras and representation theory (2006S)

Lie algebras and representation theory

8.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Erstmals am Donnerstag, 2.3.2006

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 02.03. 15:00 - 17:00 Seminarraum
  • Tuesday 07.03. 15:00 - 17:00 Seminarraum
  • Thursday 09.03. 15:00 - 17:00 Seminarraum
  • Tuesday 14.03. 15:00 - 17:00 Seminarraum
  • Thursday 16.03. 15:00 - 17:00 Seminarraum
  • Tuesday 21.03. 15:00 - 17:00 Seminarraum
  • Thursday 23.03. 15:00 - 17:00 Seminarraum
  • Tuesday 28.03. 15:00 - 17:00 Seminarraum
  • Thursday 30.03. 15:00 - 17:00 Seminarraum
  • Tuesday 04.04. 15:00 - 17:00 Seminarraum
  • Thursday 06.04. 15:00 - 17:00 Seminarraum
  • Tuesday 25.04. 15:00 - 17:00 Seminarraum
  • Thursday 27.04. 15:00 - 17:00 Seminarraum
  • Tuesday 02.05. 15:00 - 17:00 Seminarraum
  • Thursday 04.05. 15:00 - 17:00 Seminarraum
  • Tuesday 09.05. 15:00 - 17:00 Seminarraum
  • Thursday 11.05. 15:00 - 17:00 Seminarraum
  • Tuesday 16.05. 15:00 - 17:00 Seminarraum
  • Thursday 18.05. 15:00 - 17:00 Seminarraum
  • Tuesday 23.05. 15:00 - 17:00 Seminarraum
  • Tuesday 30.05. 15:00 - 17:00 Seminarraum
  • Thursday 01.06. 15:00 - 17:00 Seminarraum
  • Thursday 08.06. 15:00 - 17:00 Seminarraum
  • Tuesday 13.06. 15:00 - 17:00 Seminarraum
  • Tuesday 20.06. 15:00 - 17:00 Seminarraum
  • Thursday 22.06. 15:00 - 17:00 Seminarraum
  • Tuesday 27.06. 15:00 - 17:00 Seminarraum
  • Thursday 29.06. 15:00 - 17:00 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. We discuss the structure theory including root space decompositions and representations. We prove the theorem of Weyl, the theorems of Levi and Malcev and the Cartan criterion for semisimple Lie algebras.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

1.) Jacobson, Nathan: Lie algebras. 1962
2.) Serre, Jean-Pierre: Lie algebras and Lie groups. 1965
3.) Samelson, H.: Notes on Lie algebras. 1969
4.) Stewart, I.: Lie algebras. 1970
5.) Winter, David J.: Abstract Lie algebras. 1972
6.) Humphreys, J.E.: Introduction to Lie algebras and representation
theory. 1972
7.) Varadarajan, V.S.: Lie groups, Lie algebras, and their representations.
1974
8.) Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
9.) Bahturin, Ju.A.: Lectures on Lie algebras. 1978
10.) Onishchik, A.L.: Introduction to the theory of Lie groups and Lie
algebras. 1979
11.) Zassenhaus, Hans: Lie groups, Lie algebras and representation theory.
1981
12.) Postnikov, M.M.: Lie groups and Lie algebras. 1982
13.) Kirillov, A.A.: Representations of Lie groups and Lie algebras. 1985
14.) Wojtynski, Wojciech: Lie groups and Lie algebras. 1986
15.) Seligman, George B.: Constructions of Lie algebras and their modules.
1988
16.) Knapp, Anthony W.: Lie groups, Lie algebras, and cohomology. 1988
17.) Hilgert, Joachim; Neeb, Karl-Hermann: Lie-Gruppen und Lie-Algebren.
1991
18.) Carter, Roger: Lie algebras of finite and affine type. 2005

Association in the course directory

Last modified: Mo 07.09.2020 15:40