Homogeneous symplectic manifolds and dipolarizations in Lie algebras
type: Item
instance of: scholarly article
title: Homogeneous symplectic manifolds and dipolarizations in Lie algebras
zbMATH Open document ID: 0781.53027
author: Soji Kaneyuki
published in: Tokyo Journal of Mathematics
publication date: 1993-08-08T00:00:00Z
review text: 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.
reviewed by: Stanisław Janeczko
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 179091
zbMATH Keywords: homogeneous parakähler manifolds
zbMATH Keywords: transversal lagrangian fibrations
zbMATH Keywords: parakähler algebra
zbMATH Keywords: graded Lie algebras
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270129458
OpenAlex ID: W1969424465
DOI: 10.3836/TJM/1270129458
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description: scientific article; zbMATH DE number 179091