Dipolarizations in compact Lie algebras and homogeneous parakähler manifolds
type: Item
instance of: scholarly article
title: Dipolarizations in compact Lie algebras and homogeneous parakähler manifolds
zbMATH Open document ID: 0899.53031
author: Zixin Hou
author: Shaoqiang Deng
author: Soji Kaneyuki
published in: Tokyo Journal of Mathematics
publication date: 1998-03-18T00:00:00Z
review text: A parakähler manifold \(M\) is a symplectic manifold which admits a pair of transversal Lagrangian foliations. If a Lie group \(G\) acts transitively on \(M\) by symplectomorphisms which preserve each of the foliations, then \(M\) is called homogeneous parakähler manifold. The authors characterize homogeneous parakähler manifolds by the notion of dipolarization of compact Lie algebras. They prove that a compact semisimple Lie algebra has no nontrivial dipolarizations. They also prove that a \(G\)-invariant parakähler structure may exist on \(G/H\), where \(G\) is a connected compact Lie group and \(H\) is a closed subgroup of \(G\), if and only if \(G/H\) is an even-dimensional torus.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1130803
zbMATH Keywords: para-Kähler manifolds
zbMATH Keywords: homogeneity
zbMATH Keywords: dipolarization of Lie algebras
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042111
OpenAlex ID: W2009876850
DOI: 10.3836/TJM/1270042111
Recommended article: Q4237195
Recommended article: Dipolarizations in quadratic Lie algebras and homogeneous parak$auml$hler manifolds
Recommended article: Homogeneous symplectic manifolds and dipolarizations in Lie algebras
Recommended article: Q5476072
Recommended article: Q4547973
Recommended article: Q4300441
Recommended article: Dipolarizations in Kac–Moody Algebras
Recommended article: Para-Kähler hom-Lie algebras
Recommended article: Complex and Kähler structures on hom-Lie algebras
Recommended article: Realization of compact Lie algebras in Kahler manifolds
description: scientific article; zbMATH DE number 1130803