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Nilpotent Orbits
Nilpotente Bahnen
Last Updated: 2026-02-05 15:29:11
Abstract
Semisimple and nilpotent adjoint orbits. Dynkin-Kostant classification of nilpotent orbits with the theorem of Jacobson-Mozorov. Classical cases (partitions). Weighted Dynkin diagrams. The exceptional Lie algebras.
Content
Semisimple and nilpotent elements of Lie algebras, adjoint and coadjoint orbits. Classification of semisimple orbits. Dynkin-Kostant classification of nilpotent orbits: Theorem of Jacobson-Mozorov, Theorems of Kostant, Mal'cev, weighted Dynkin diagrams, parabolic subalgebras. Regular, subregular and minimal nilpotent orbit. Classical case. Exceptional Lie algebras: Levi subalgebras, distinguished nilpotent orbits.
Resources
Literature
The course is based on D. Collingwood, W. McGovern: Nilpotent orbits in semisimple Lie algebras Van Nostrand Reinhold Co., New York, 1993. xiv+186 pp. ISBN: 0-534-18834-6
General Information
- Language
- German
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Nilpotente Bahnen |
|
3 h weekly |