On para-Kähler and hyper-para-Kähler Lie algebras

DOI10.1016/j.jalgebra.2015.04.015zbMath1440.17002arXiv1312.2078OpenAlexW2073264801WikidataQ115350850 ScholiaQ115350850MaRDI QIDQ2345560

Saïd Benayadi, Mohamed Boucetta

Publication date: 22 May 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.2078

zbMATH Keywords

symplectic Lie algebra\(S\)-matrixleft symmetric algebrahyper-para-Kähler Lie algebrapara-Kähler Lie algebra

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Structure theory for Lie algebras and superalgebras (17B05) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Solvable, nilpotent (super)algebras (17B30)

Related Items (16)

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 ⋮ COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS ⋮ Contravariant pseudo-Hessian manifolds and their associated Poisson structures ⋮ Bi-Lagrangian structures on nilmanifolds ⋮ Indefinite hyperkähler metrics on Lie groups with abelian complex structures ⋮ 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 ⋮ Bi-Lagrangian structure on the symplectic affine Lie algebra of \(\mathbb{R}^2\) ⋮ Pre-symplectic algebroids and their applications ⋮ (para-) Kähler structures on \(\rho \)-commutative algebras ⋮ Product and complex structures on hom-Lie superalgebras ⋮ The classification of left-invariant para-Kähler structures on simply connected four-dimensional Lie groups ⋮ Nijenhuis operators on pre-Lie algebras ⋮ On k-para-Kähler Lie algebras, a subclass of k-symplectic Lie algebras

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