Abelian para-Kaehler structures on Lie algebras

Para-Kaehler Lie algebras which decompose as the sum of two abelian Lagrangian subalgebras are studied. We propose several constructions and provide an inductive description of such Lie algebras. The curvatures of the para-Kaehler metric are computed and sufficient conditions to ensure flatness or R...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 29; no. 2; pp. 160 - 173
Main Authors Bajo, Ignacio, Benayadi, Saied
Format Journal Article
LanguageEnglish
Published 01.01.2011
Subjects
Computation
Construction
Curvature
Decomposition
Differential geometry
Flatness
Lie groups
Mathematical analysis
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Summary:Para-Kaehler Lie algebras which decompose as the sum of two abelian Lagrangian subalgebras are studied. We propose several constructions and provide an inductive description of such Lie algebras. The curvatures of the para-Kaehler metric are computed and sufficient conditions to ensure flatness or Ricci-flatness are given. The Lie algebras for which the para-Kaehler metric is Einstein and non-Ricci-flat are completely characterized.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0926-2245
DOI:10.1016/j.difgeo.2011.02.003