Hyper-para-Kähler Lie algebras with abelian complex structures and their classification up to dimension 8
type: Item
instance of: scholarly article
title: Hyper-para-Kähler Lie algebras with abelian complex structures and their classification up to dimension 8
zbMATH Open document ID: 1398.53034
author: Ignacio Bajo
author: Esperanza Sanmartín
published in: Annals of Global Analysis and Geometry
publication date: 2018-06-26T00:00:00Z
review text: In the paper under review the authors consider the hyper-para-Kähler algebras \(\mathfrak{g}\) whose complex structure \(J\) is abelian, that is, the eigenspaces of \(J\) in the complexification of \(\mathfrak{g}\) are abelian Lie algebras. These algebras are characterized in terms of certain triples consisting of an associative, commutative algebra \(V\) such that \(V^{3} = \{ 0 \}\), a skew-symmetric form on it, and a semilinear map. This allows the authors to give a classification of hyper-para-Kähler algebras of dimension \(8\), and of those of arbitrary dimension for which \(V^{2}\) has dimension one.
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 6894771
zbMATH Keywords: hyper-para-Kähler manifold
zbMATH Keywords: abelian (para)complex structure
zbMATH Keywords: symplectic left-symmetric algebra
MaRDI profile type: Publication
full work available at URL: s10455-017-9587-8
OpenAlex ID: W2772900045
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DOI: 10.1007/S10455-017-9587-8
description: scientific article; zbMATH DE number 6894771