Dipolarizations in quadratic Lie algebras and homogeneous parak$auml$hler manifolds

Abstract

A Lie algebra with a nondegenerate symmetric and invariant bilinear form is called quadratic. A dipolarization in a Lie algebra is the two polarizations ± in at a common linear form on satisfying = + + −. In this paper, we study dipolarizations in extended Heisenberg algebras, a subclass of quadratic Lie algebras, and homogeneous parakähler manifolds associated with these dipolarizations.