Abelian para-Kähler structures on Lie algebras

DOI10.1016/j.difgeo.2011.02.003zbMath1221.53110OpenAlexW2021836394WikidataQ115356975 ScholiaQ115356975MaRDI QIDQ531732

Ignacio Bajo, Saïd Benayadi

Publication date: 19 April 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.02.003

zbMATH Keywords

symplectic Lie algebracurvaturesymplectic double extension

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Solvable, nilpotent (super)algebras (17B30)

Related Items

Nearly para-Kähler geometry on Lie groups ⋮ Symplectic, product and complex structures on 3-Lie algebras ⋮ Hyper-para-Kähler Lie algebras with abelian complex structures and their classification up to dimension 8 ⋮ Symplectic double extensions for restricted quasi-Frobenius Lie (super)algebras ⋮ Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras ⋮ Indefinite hyperkähler metrics on Lie groups with abelian complex structures ⋮ Geometry of four-dimensional Kähler and para-Kähler Lie groups ⋮ Symplectic structures, product structures and complex structures on Leibniz algebras ⋮ Quasi-triangular pre-Lie bialgebras, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras ⋮ (para-) Kähler structures on \(\rho \)-commutative algebras ⋮ Abelian Hermitian geometry ⋮ Nijenhuis operators on pre-Lie algebras ⋮ Symplectic Jacobi-Jordan algebras ⋮ On k-para-Kähler Lie algebras, a subclass of k-symplectic Lie algebras ⋮ On para-Kähler and hyper-para-Kähler Lie algebras

Cites Work

• Double products and hypersymplectic structures on \(\mathbb R^{4n}\)
• Radical d'une algèbre symétrique à gauche
• Symplectic or contact structures on Lie groups
• Families of strong KT structures in six dimensions
• Symplectic double extension of a symplectic Lie group
• Symplectic structures on quadratic Lie algebras
• Product structures on four dimensional solvable Lie algebras
• Homogeneous para-Kähler Einstein manifolds
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