Studying dipolarizations reveals insights into semisimple Lie algebras and parakahler manifolds, implying deeper geometric connections.
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.
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Hou et al. (1999) studied this question.