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Integration of holomorphic Lie algebroids

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Abstract

We prove that a holomorphic Lie algebroid is integrable if and only if its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic–Fernandes (Theorem 4.1 in Crainic, Fernandes in Ann Math 2:157, 2003) do also apply in the holomorphic context without any modification. As a consequence we prove that a holomorphic Poisson manifold is integrable if and only if its real part or imaginary part is integrable as a real Poisson manifold.

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Authors and Affiliations

  1. Département de mathématiques, Université de Poitiers, 86962, Futuroscope-Chasseneuil, France

    Camille Laurent-Gengoux

  2. Departement Mathematik, E.T.H. Zürich, 8092, Zurich, Switzerland

    Mathieu Stiénon

  3. Department of Mathematics, Penn State University, University Park, PA, 16802, USA

    Ping Xu

Authors
  1. Camille Laurent-Gengoux
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  2. Mathieu Stiénon
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  3. Ping Xu
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Corresponding author

Correspondence to Ping Xu.

Additional information

Mathieu Stiénon’s research was supported by the European Union through the FP6 Marie Curie R.T.N. ENIGMA (Contract number MRTN-CT-2004-5652). Ping Xu’s research was partially supported by NSF grants DMS-0306665 and DMS-0605725 & NSA grant H98230-06-1-0047.

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Laurent-Gengoux, C., Stiénon, M. & Xu, P. Integration of holomorphic Lie algebroids. Math. Ann. 345, 895–923 (2009). https://doi.org/10.1007/s00208-009-0388-7

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  • DOI: https://doi.org/10.1007/s00208-009-0388-7

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