Properties
- Nilpotent orbits can be characterized as those orbits of the adjoint action whose Zariski closure contains 0.
- Nilpotent orbits are finite in number.
- The Zariski closure of a nilpotent orbit is a union of nilpotent orbits.
- Jacobson–Morozov theorem: over a field of characteristic zero, any nilpotent element e can be included into an sl2-triple {e,h,f} and all such triples are conjugate by ZG(e), the centralizer of e in G. Together with the representation theory of sl2, this allows one to label nilpotent orbits by finite combinatorial data, giving rise to the Dynkin–Kostant classification of nilpotent orbits.
Read more about this topic: Nilpotent Orbit
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