Orbits in real $\Z_m$-graded semisimple Lie algebras

Details Orbits in real $\Z_m$-graded semisimple Lie algebras Orbits in real $\Z_m$-graded semisimple Lie algebras

2009-05-18

arxiv.org/abs/0905.2939v5

Journal of Lie Theory, 21(2011), 285-305

Mathematics

Representation Theory

19 pages, misprints are corrected, final version

Scientific paper

In this note we propose a method to classify homogeneous nilpotent elements
in a real $Z_m$-graded semisimple Lie algebra $g$. Using this we describe the
set of orbits of homogeneous elements in a real $Z_2$-graded semisimple Lie
algebra. A classification of 4-vectors (resp. 4-forms) on $R^8$ can be given
using this method.

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