## Journal of Generalized Lie Theory and Applications

### Properties of Nilpotent Orbit Complexification

Peter Crooks

#### Abstract

We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are incomparable in the closure order. Secondly, we characterize those $\mathfrak{g}$ having non-empty intersections with all nilpotent orbits in $\mathfrak{g}_{\mathbb{C}}$. Finally, for $\mathfrak{g}$ quasi-split, we characterize those complex nilpotent orbits containing real ones.

#### Article information

Source
J. Gen. Lie Theory Appl. Volume 10, Number S2 (2016), pages.

Dates
First available in Project Euclid: 16 November 2016