Examples of compact Lefschetz solvmanifolds.
type: Item
instance of: scholarly article
title: Examples of compact Lefschetz solvmanifolds.
zbMATH Open document ID: 1047.53050
author: Takumi Yamada
published in: Tokyo Journal of Mathematics
publication date: 2002-01-01T00:00:00Z
review text: A symplectic manifold \((M^{2m},\omega)\) is called a Lefschetz manifold if the mapping \(\wedge\omega^{m-1}: H^1_{DR}\to H^{2m-1}_{DR}\) on \(M\) is an isomorphism. By a solvmanifold is meant a homogeneous space \(G/\Gamma\) where \(G\) is a simply connected solvable Lie group and \(\Gamma\) is a lattice. A solvable Lie algebra \({\mathfrak g}\) is said to be completely solvable if \(\text{ad}(X)\) has only real eigenvalues for every \(X\in{\mathfrak g}\). The purpose of this paper is to present examples of higher-dimensional completely solvable Lie groups which admit lattices and compact Lefschetz solvmanifolds. It extends also to the construction of compact symplectic solvmanifolds with the property known as Hard-Lefschetz's.
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1930964
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: lattice
zbMATH Keywords: solvable Lie group
reviewed by: Tanjiro Okubo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208853
OpenAlex ID: W2030540172
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DOI: 10.3836/TJM/1244208853
description: scientific article; zbMATH DE number 1930964