Journal of Lie Theory 21 (2011), No. 2, 285--305
Copyright Heldermann Verlag 2011
Orbits in Real Zm-Graded Semisimple Lie Algebras
Hông Vân Le
Mathematical Institute, Academy of Sciences, Zitna 25, 11567 Praha 1, Czech Republic
hvle@math.cas.cz
We propose a method to classify homogeneous nilpotent elements in a real Zm-graded semisimple Lie algebra g. Using this we describe the set of orbits of homogeneous elements in a real Z2-graded semisimple Lie algebra. A classification of 4-vectors (resp. 4-forms) on R8 can be given using this method.
Keywords: Real Z-sub-m-graded Lie algebra, nilpotent elements, homogeneous elements.
MSC: 17B70, 15A72, 13A50
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