Dipolarizations in semisimple Lie algebras and homogeneous parakmanifolds

A dipolarization in a Lie algebra g is two polarizations g in g at a common linear form on g satisfying g=g + +g . We study dipolarizations in semisimple Lie algebras, especially, the relation between dipolarizations and gradations. As an application, we give a relation between semisimple homogeneous parakhler manifolds and hyperbolic semisimple orbits. For g real semisimple, we determine the characteristic elements, from which dipolarizations can be constructed.