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Displaying similar documents to “A complete classification of four-dimensional paraKähler Lie algebras”

Homogeneous Riemannian manifolds with generic Ricci tensor

Włodzimierz Jelonek (2001)

Annales Polonici Mathematici

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We describe homogeneous manifolds with generic Ricci tensor. We also prove that if 𝔤 is a 4-dimensional unimodular Lie algebra such that dim[𝔤,𝔤] ≤ 2 then every left-invariant metric on the Lie group G with Lie algebra 𝔤 admits two mutually opposite compatible left-invariant almost Kähler structures.

Some properties of para-Kähler-Walker metrics

Mustafa Özkan, Murat İşcan (2014)

Annales Polonici Mathematici

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A Walker 4-manifold is a pseudo-Riemannian manifold (M₄,g) of neutral signature, which admits a field of parallel null 2-planes. We study almost paracomplex structures on 4-dimensional para-Kähler-Walker manifolds. In particular, we obtain conditions under which these almost paracomplex structures are integrable, and the corresponding para-Kähler forms are symplectic. We also show that Petean's example of a nonflat indefinite Kähler-Einstein 4-manifold is a special case of our constructions. ...

Homogeneous quaternionic Kähler structures on Alekseevskian 𝒲-spaces

Wafaa Batat, P. M. Gadea, Jaime Muñoz Masqué (2012)

Annales Polonici Mathematici

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The homogeneous quaternionic Kähler structures on the Alekseevskian 𝒲-spaces with their natural quaternionic structures, each of these spaces described as a solvable Lie group, and the type of such structures in Fino's classification, are found.

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

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We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

Lie Algebra bundles on s-Kähler manifolds, with applications to Abelian varieties

Giovanni Gaiffi, Michele Grassi (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that one can obtain natural bundles of Lie algebras on rank two s -Kähler manifolds, whose fibres are isomorphic respectively to so ( s + 1 , s + 1 ) , su ( s + 1 , s + 1 ) and sl ( 2 s + 2 , ℝ ) . These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of Kähler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of su ( s + 1 , s + 1 ) on (rational) Hodge classes of Abelian varieties with rational period matrix.