alexa Properties of Nilpotent Orbit Complexification
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
Open Access

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Research Article

Properties of Nilpotent Orbit Complexification

Peter Crooks*

Department of Mathematics, University of Toronto, Canada

*Corresponding Author:
Peter Crooks
Department of Mathematics
University of Toronto, Canada
E-mail: [email protected]

Received Date: April 24, 2016; Accepted Date: June 09, 2016; Published Date: June 30, 2016

Citation: Crooks P (2016) Properties of Nilpotent Orbit Complexification. J Generalized Lie Theory Appl S2:012. doi:10.4172/1736-4337.S2-012

Copyright: © 2016 Crooks P. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

We consider aspects of the relationship between nilpotent orbits in a semisim-ple real Lie algebra g and those in
its complexification g. 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 g having non-empty intersections with all nilpotent
orbits in g. Finally, for g quasi-split, we characterize those complex nilpotent orbits containing real ones.

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