Orbits in real ${\mathbb{Z}}_m$-graded semisimple Lie algebras

Abstract

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.

19 pages, misprints are corrected, final version

References in corpus (1)

• The geometry of three-forms in six and seven dimensions