The Sylvester's law of inertia in simple graded Lie algebras (Q1277286)

Let \(L=L_{-1}\oplus L_0\oplus L_1\) be a real simple graded Lie algebra, \(G_0\) the group of automorphisms of \(L\), preserving the grading, \(G_0^0\) the identity component of \(G_0\). The main result of the paper in Theorem 5.5 gives a classification of orbits of \(G_0\) and \(G_0^0\) in \(L_{-1}\). There exist two open orbits of \(G_0^0\) which are diffeomorphic. There is a single open orbit of \(G_0\) in \(L_{-1}\).