Extending invariant complex structures

Campoamor-Stursberg, Rutwig; Cardoso, Isolda; Ovando, Gabriela P.

doi:10.1142/s0129167x15500962

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Lie algebras carrying a complex product structure are closely related to many important fields in mathematics and mathematical physics, such as Rota-Baxter operators on pre-Lie algebras [11], geometric structures on compact complex surfaces that are related to the split quaternions [7], paraquaternionic Kähler structures [5] and nilpotent Lie algebras [2]. Recently, complex product structures have been extensively investigated in [4,6,19].…”

Section: Introductionmentioning

confidence: 99%

Complex Product Structures on Hom-Lie Algebras

Nourmohammadifar¹,

Peyghan²

2018

Glasgow Math. J.

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In this paper, we introduce the notion of complex product structures on hom-Lie algebras and show that a hom-Lie algebra carrying a complex product structure is a double hom-Lie algebra and it is also endowed with a hom-left symmetric product. Moreover, we show that a complex product structure on a hom-Lie algebra determines uniquely a left symmetric product such that the complex and the product structures are invariant with respect to it. Finally, we introduce the notion of hyper-para-Kähler hom-Lie algebras and we present an example of hyper-para-Kähler hom-Lie algebras.

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Section: Introductionmentioning

confidence: 99%

Complex Product Structures on Hom-Lie Algebras

Nourmohammadifar¹,

Peyghan²

2018

Glasgow Math. J.

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From almost (para)-complex structures to affine structures on Lie groups

Calvaruso

Ovando

2017

manuscripta math.

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Let G = H ⋉ K denote a semidirect product Lie group with Lie algebra g = h⊕k, where k is an ideal and h is a subalgebra of the same dimension as k. There exist some natural split isomorphisms S with S 2 = ± Id on g: given any linear isomorphism j : h → k, we get the almost complex structure J(x, v) = (−j −1 v, jx) and the almost paracomplex structure E(x, v) = (j −1 v, jx). In this work we show that the integrability of the structures J and E above is equivalent to the existence of a left-invariant torsionfree connection ∇ on G such that ∇J = 0 = ∇E and also to the existence of an affine structure on H. Applications include complex, paracomplex and symplectic geometries.2010 Mathematics Subject Classification. 53C15, 53C55, 53D05, 22E25, 17B56.

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Pseudo-Kähler and hypersymplectic structures on semidirect products

Conti,

Gil-García

2025

Differential Geometry and its Applications

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Extending invariant complex structures

Cited by 4 publications

References 27 publications

Complex Product Structures on Hom-Lie Algebras

Complex Product Structures on Hom-Lie Algebras

From almost (para)-complex structures to affine structures on Lie groups

Pseudo-Kähler and hypersymplectic structures on semidirect products

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