240153 Lie Algebras and Lie Groups (V) (SoSe 2023)
Contents, comment
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Lie groups are groups with a differentiable manifold structure such that the group operations are compatible with the manifold structure. As key tools in the description of continuous symmetries they are ubiquitous in mathematics, but also play a role in mathematical physics.
One may associate to a Lie group a Lie algebra -- explicitly constructible as the group's tangent space at the identity element --, which captures much of the "local" structure. "Exponential" and "logarithm" maps translate between Lie groups and their associated Lie algebra, facilitating a sort of transfer of several problems about Lie groups in the (linear) realm of Lie algebras.
One of the main objectives of the course will be the classification of (complex, say) simple Lie algebras in terms of Dynkin diagrams, one of the most pervasive results of modern algebra.
Bibliography
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1. J. Tits, Liesche Gruppen und Algebren, Springer-Verlag, 1983
2. J. Hilgert, K.-H. Neeb, Structure and geometry of Lie groups, Springer Monographs in Mathematics, 2012
3. K. Erdman, M. J. Wildon, Introduction to Lie Algebras, Springer, 2006
Teaching staff
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period |
|---|
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-P1 Profilierung 1 | Profilierungsvorlesung (mit Übung) - Typ 1 | Student information | |
| 24-M-P1a Profilierung 1 Teil A | Profilierungsvorlesung (mit Übung) - Typ 1 | Student information | |
| - | Graded examination | Student information | |
| 24-M-P1b Profilierung 1 Teil B | Profilierungsvorlesung (mit Übung) - Typ 1 | Student information | |
| - | Graded examination | Student information | |
| 24-M-P2 Profilierung 2 | Profilierungsvorlesung (mit Übungen) - Typ 1 | Student information | |
| 24-M-PWM Profilierung Wirtschaftsmathematik | Profilierungsvorlesung (mit Übung) - Typ 1 | Student information | |
| - | Graded examination | Student information | |
| 24-M-S2-AL Spezialisierung 2 - Algebra | Masterkurs 1 Algebra - Variante 1 | Student information | |
| 24-M-V2-AL Vertiefung 2 - Algebra | Masterkurs 1 Algebra - Variante 1 | Student information | |
| - | Graded examination | Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Studieren ab 50 |
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- 13 Students to be reached directly via email
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- Last update basic details/teaching staff:
- Friday, January 27, 2023
- Last update times:
- Wednesday, May 3, 2023
- Last update rooms:
- Wednesday, May 3, 2023
- Type(s) / SWS (hours per week per semester)
- V / 4
- Language
- This lecture is taught in english
- Department
- Faculty of Mathematics
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