Homogeneous Hypercomplex Structures I–the Compact Lie Groups

Dimitrov, George; Tsanov, Vasil

doi:10.1007/s00031-016-9367-8

Cited by 3 publications

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“…Recently it was proven in [6] that all invariant hypercomplex structures arise in this way, and in [2] it was proven under the additional restriction of compatibility with the bi-invariant metric. We present here a short description following [6]. For a compact Lie algebra g with semisimple part g, fix a Cartan subalgebra h of g C .…”

Section: Poisson Structures On Hkt Manifolds and Their Twistor Spacementioning

confidence: 99%

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Poisson structures on twistor spaces of hyperkähler and HKT manifolds

Grantcharov

Hernandez-Vazquez

2015

Journal of Geometry and Physics

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Abstract. We characterize HKT structures in terms of a nondegenrate complex Poisson bivector on a hypercomplex manifold. We extend the characterization to the twistor space. After considering the flat case in detail, we show that the twistor space of a hyperkähler manifold admits a holomorphic Poisson structure. We briefly mention the relation to quaternionic and hypercomlex deformations on tori and K3 surfaces.

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Section: Poisson Structures On Hkt Manifolds and Their Twistor Spacementioning

confidence: 99%

“…For a compact Lie algebra g with semisimple part g, fix a Cartan subalgebra h of g C . Choose a set of positive roots R and a basis Π of R. The following definition is from [6]:…”

Section: Poisson Structures On Hkt Manifolds and Their Twistor Spacementioning

confidence: 99%

Poisson structures on twistor spaces of hyperkähler and HKT manifolds

Grantcharov

Hernandez-Vazquez

2015

Journal of Geometry and Physics

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Homogeneous hypercomplex structures II - Coset spaces of compact Lie groups

Dimitrov

Tsanov

2021

Journal of Geometry and Physics

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A remark on the quaternionic Monge-Ampère equation on foliated manifolds

Gentili

Vezzoni

2022

Proc. Amer. Math. Soc.

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Pursuing the approach of Gentili and Vezzoni [Math. Res. Not. IMRN 12 (2022), pp. 9499–9528] we study the quaternionic Monge-Ampère equation on HKT (hyperkähler with torsion) manifolds admitting an HKT foliation having corank 4 4 . We show that in this setting the quaternionic Monge-Ampère equation has always a unique solution for every basic datum. This approach includes the study of the equation on SU ⁡ ( 3 ) \operatorname {SU}(3) .

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Homogeneous Hypercomplex Structures I–the Compact Lie Groups

Abstract: Abstract. We obtain a complete list of homogeneous hypercomplex structures on the compact Lie groups. The substantial results are formulated and proved entirely in terms of the structure theory of Lie groups and algebras.

Cited by 3 publications

References 24 publications

Poisson structures on twistor spaces of hyperkähler and HKT manifolds

Poisson structures on twistor spaces of hyperkähler and HKT manifolds

Homogeneous hypercomplex structures II - Coset spaces of compact Lie groups

A remark on the quaternionic Monge-Ampère equation on foliated manifolds

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