an:05883433
Zbl 1228.17025
Lê, Hông Vân
Orbits in real \(\mathbb Z_{m}\)-graded semisimple Lie algebras
EN
J. Lie Theory 21, No. 2, 285-305 (2011).
0949-5932
2011
j
17B70 15A72 13A50
real \({\mathbb Z}_m\)-graded Lie algebra; nilpotent elements; homogeneous elements
A method to classify homogeneous nilpotent elements in a real \({\mathbb Z}_{m}\)-graded semisimple Lie algebra is proposed. This consists first in a classification of the conjugacy classes of characteristics (this makes use among others of work by \textit{E.~B.~Vinberg} [Sel. Math. Sov. 6, 15--35 (1987; Zbl 0612.17010)]), and then in classifying the conjugacy classes of nilpotent elements associated with a given conjugacy class of a characteristic.
Using work of \textit{T.~Oshima} and \textit{T.~Matsuki} [J. Math. Soc. Japan 32, 399--414 (1980; Zbl 0451.53039)], this is applied to describe the set of orbits of homogeneous elements of degree \(1\) in a \({\mathbb Z}_{2}\)-graded semisimple Lie algebra, following a scheme proposed by \textit{A.~G.~Elashvili} and \textit{Vinberg} [Sel. Math. Sov. 7, No. 1, 63--98 (1988; Zbl 0648.15021)].
A. Caranti (Trento)
0612.17010; 0451.53039; 0648.15021