250126 VO Lie Algebras and Representation Theory (2024W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Wednesday 02.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 03.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 09.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 10.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 16.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 17.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 23.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 24.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 30.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 31.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 06.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 07.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 13.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 14.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 20.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 21.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 27.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 28.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- N Wednesday 04.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 05.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 11.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 12.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 08.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 09.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 15.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 16.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 22.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Thursday 23.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 29.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
The lecture gives an introduction to the structure theory and representation theory of Lie algebras. The main focus lies on the classification of finite-dimensional complex semisimple Lie algebras and their finite-dimensional representations.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, Number Theory and many other areas. The lecture mainly uses a blackboard.After introducing basic notions of Lie algebra theory we discuss the theorems of Engel and Lie, the Jordan-Chevalley decomposition, the Cartan criteria, Weyl's theorem, the theorems of Levi and Malcev, the classification of complex semisimple Lie algebras and Serre's theorem. In the chapter on representations of semisimple Lie algebras we present the classification by highest weight, introducing also the universal enveloping algebra. We give several applications such as Weyl's character formula and Weyl's dimension formula.
Assessment and permitted materials
There will be a written exam after the end of the lecture. No aids are allowed.
Minimum requirements and assessment criteria
50 % of the points for the written exam.
Examination topics
All major topics covered in the lecture.
Reading list
[1] Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
[2] Fulton, William: Harris,Joe: Representation Theory. 2004
[3] A. Henderson: Representations of Lie Algebras. 2012
[4] Humphreys, James. E.: Introduction to Lie algebras and representation theory. 1972
[5] Jacobson, Nathan: Lie algebras. 1962
[6] Kirillov, A.A.: Representations of Lie groups and Lie algebras. 1985
[7] Knapp, Anthony W.: Lie Groups: Beyond an Introduction. 2002
[8] Serre, Jean-Pierre: Complex semisimple Lie algebras. 1987
[9] Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. 1974
[10] Winter, David J.: Abstract Lie algebras. 1972
[2] Fulton, William: Harris,Joe: Representation Theory. 2004
[3] A. Henderson: Representations of Lie Algebras. 2012
[4] Humphreys, James. E.: Introduction to Lie algebras and representation theory. 1972
[5] Jacobson, Nathan: Lie algebras. 1962
[6] Kirillov, A.A.: Representations of Lie groups and Lie algebras. 1985
[7] Knapp, Anthony W.: Lie Groups: Beyond an Introduction. 2002
[8] Serre, Jean-Pierre: Complex semisimple Lie algebras. 1987
[9] Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. 1974
[10] Winter, David J.: Abstract Lie algebras. 1972
Association in the course directory
MGEV; MALV
Last modified: Tu 05.11.2024 14:26