Orbits in real Z_M-graded semisimple Lie algebras

摘要

In this note we propose a method to classify homogeneous nilpo-tent 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 semisim-ple Lie algebra. A classification of 4-vectors (resp. 4-forms) on R~8 can be given using this method.