Universität Wien
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878194 VO Lie-Algebren und Darstellungstheorie (2004W)

Lie-Algebren und Darstellungstheorie

0.00 ECTS (4.00 SWS), UG02 SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 05.10. 17:00 - 18:30 Seminarraum
  • Wednesday 06.10. 17:00 - 18:30 Seminarraum
  • Tuesday 12.10. 17:00 - 18:30 Seminarraum
  • Wednesday 13.10. 17:00 - 18:30 Seminarraum
  • Tuesday 19.10. 17:00 - 18:30 Seminarraum
  • Wednesday 20.10. 17:00 - 18:30 Seminarraum
  • Tuesday 26.10. 17:00 - 18:30 Seminarraum
  • Wednesday 27.10. 17:00 - 18:30 Seminarraum
  • Wednesday 03.11. 17:00 - 18:30 Seminarraum
  • Tuesday 09.11. 17:00 - 18:30 Seminarraum
  • Wednesday 10.11. 17:00 - 18:30 Seminarraum
  • Tuesday 16.11. 17:00 - 18:30 Seminarraum
  • Wednesday 17.11. 17:00 - 18:30 Seminarraum
  • Tuesday 23.11. 17:00 - 18:30 Seminarraum
  • Wednesday 24.11. 17:00 - 18:30 Seminarraum
  • Tuesday 30.11. 17:00 - 18:30 Seminarraum
  • Wednesday 01.12. 17:00 - 18:30 Seminarraum
  • Tuesday 07.12. 17:00 - 18:30 Seminarraum
  • Tuesday 14.12. 17:00 - 18:30 Seminarraum
  • Wednesday 15.12. 17:00 - 18:30 Seminarraum
  • Tuesday 11.01. 17:00 - 18:30 Seminarraum
  • Wednesday 12.01. 17:00 - 18:30 Seminarraum
  • Tuesday 18.01. 17:00 - 18:30 Seminarraum
  • Wednesday 19.01. 17:00 - 18:30 Seminarraum
  • Tuesday 25.01. 17:00 - 18:30 Seminarraum
  • Wednesday 26.01. 17:00 - 18:30 Seminarraum

Information

Aims, contents and method of the course

The first chapter of this lecture introduces the elementary concepts and the basic definitions: Lie algebras, representations, modules,
derivations, associative algebras, Poisson algebras, Lie groups, the exponential function etc. In the second chapter we deal with semisimple and reductive Lie algebras.
We discuss the structure theory including root space decompositions and modules. We prove the theorem of Weyl, the theorems of Levi and Malcev and the Cartan criterion for semisimple Lie algebras. The third chapter deals with solvable and nilpotent Lie algebras. We prove
the theorems of Engel and Lie, and the solvability criterion of Cartan. The last chapter gives an overview of Lie algebra cohomology.

Assessment and permitted materials

Minimum requirements and assessment criteria

This lecture should give a broad introduction into the area of Lie algebras and their representations. These topics arise in many other areas of geometry, algebra and number theory. The lecture intends to give the
students the necessary background.

Examination topics

not yet available, see methods in german.

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.) Kaplansky, Irving: Lie algebras and locally compact groups. 1971
6.) Winter, David J.: Abstract Lie algebras. 1972
7.) Humphreys, J.E.: Introduction to Lie algebras and representation theory.
1972
8.) Sagle, Arthur A.; Walde, Ralph E.: Introduction to Lie groups and Lie algebras. 1973
9.) Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. 1974
10.) Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
11.) Wan, Zhe-Xian: Lie algebras. 1975
12.) Goto, Morikuni; Grosshans, Frank D.: Semisimple Lie algebras. 1978
13.) Bahturin, Ju.A.: Lectures on Lie algebras. 1978
14.) Onishchik, A.L.: Introduction to the theory of Lie groups and Lie algebras. 1979
15.) Zassenhaus, Hans: Lie groups, Lie algebras and representation theory. 1981
16.) Hochschild, Gerhard P.: Basic theory of algebraic groups and Lie algebras. 1981
17.) Postnikov, M.M.: Lie groups and Lie algebras. 1982
18.) Kirillov, A.A.: Representations of Lie groups and Lie algebras. 1985
19.) Wojtynski, Wojciech: Lie groups and Lie algebras. 1986
20.) Seligman, George B.: Constructions of Lie algebras and their modules. 1988
21.) Knapp, Anthony W.: Lie groups, Lie algebras, and cohomology. 1988
22.) Strade, Helmut; Farnsteiner, Rolf: Modular Lie algebras and their representations. 1988
23.) Hilgert, Joachim; Neeb, Karl-Hermann: Lie-Gruppen und Lie-Algebren. 1991
24.) Reutenauer, Christophe: Free Lie algebras. 1993
25.) Roggenkamp, Klaus W.: Cohomology of Lie-algebras, groups and algebras. 1994
26.) Carter, Roger; Segal, Graeme; Macdonald, Ian: Lectures on Lie groups and Lie algebras. 1995
27.) de Graaf, Willem A.: Lie algebras: Theory and algorithms. 2000
28.) Onishchik, Arkady L.: Lectures on real semisimple Lie algebras and their representations. 2004

Association in the course directory

Currently no association information is available.

Last modified: Mo 07.09.2020 15:50