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250048 VO Lie Algebras and Representation Theory (2021S)
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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
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Monday
01.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
04.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
08.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
11.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
15.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
18.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
22.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
25.03.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
12.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
15.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
19.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
22.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
26.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
29.04.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
03.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
06.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
10.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
17.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
20.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
27.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
31.05.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
07.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
10.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
14.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
17.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
21.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Thursday
24.06.
15:00 - 16:30
Digital
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
28.06.
15:00 - 16:30
Digital
Seminarraum 11 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 here lies on the classification of finite-dimensional complex semisimple Lie algebras and their 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.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
Written exam after the end of the lecture.
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: Fr 12.05.2023 00:21