Properties of Nilpotent Orbit Complexification
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.
We consider aspects of the relationship between nilpotent orbits in a semisim-ple real Lie algebra g and those in
its complexification gïÃ¯Â¿Â½Ã¯Â¿Â½. 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 gïÃ¯Â¿Â½Ã¯Â¿Â½. Finally, for g quasi-split, we characterize those complex nilpotent orbits containing real ones.