alexa Abstract | Properties of Nilpotent Orbit Complexification
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article Open Access

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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Author(s): Peter Crooks

Keywords

Nilpotent orbit, Quasi-split Lie algebra, Kostant- Sekiguchi correspondence, Algebra, Combinatorics, Deformations Theory, Geometry, Harmonic Analysis, Homological Algebra, Homotopical Algebra, Latin Squares, Lie Theory, Lie Triple Systems, Loop Algebra, Operad Theory, Quantum Group, Quasi-Group, Representation theory, Super Algebras, Lie Superalgebra, Symmetric Spaces, Topologies, Lie Algebra

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