Homogeneous symplectic manifolds and dipolarizations in Lie algebras
The author gives an algebraic method of constructing the homogeneous parakähler manifolds introduced originally by [\textit{P. Libermann}, Sur le problème d'équivalence de certaines structures infinitesimales, Ann. Math. Pura Appl., IV. Ser. 36, 27-120 (1954; Zbl 0056.154)]. A parakähler manifold is a symplectic manifold with a distinguished pair of transversal lagrangian fibrations. The author generalizes the notion of Kähler algebra introducing the parakähler algebra playing an analogous role in parakähler manifold theory. Using the dipolarization techniques he studies homogeneous parakähler manifolds which are obtained from semisimple graded Lie algebras.
scientific article; zbMATH DE number 179091