Hyper-para-Kähler Lie algebras with abelian complex structures and their classification up to dimension 8

DOI10.1007/s10455-017-9587-8zbMath1398.53034OpenAlexW2772900045MaRDI QIDQ1647726

Esperanza Sanmartín, Ignacio Bajo

Publication date: 26 June 2018

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-017-9587-8

zbMATH Keywords

abelian (para)complex structurehyper-para-Kähler manifoldsymplectic left-symmetric algebra

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Global differential geometry of Hermitian and Kählerian manifolds (53C55) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Solvable, nilpotent (super)algebras (17B30)

Related Items (3)

Indefinite hyperkähler metrics on Lie groups with abelian complex structures ⋮ Symplectic structures, product structures and complex structures on Leibniz algebras ⋮ Symmetric and skew-symmetric complex structures

Cites Work

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• Abelian para-Kähler structures on Lie algebras
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• On the nilpotent Lie algebras of dimension \(\leq 7)\)
• Radical d'une algèbre symétrique à gauche
• Hypercomplex eight-dimensional nilpotent Lie groups.
• Neutral Calabi-Yau structures on Kodaira manifolds
• On para-Kähler and hyper-para-Kähler Lie algebras
• Hypersymplectic Lie algebras
• Toric hypersymplectic quotients
• Complex product structures on Lie algebras

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