Integration of Holomorphic Lie Algebroids

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 do also apply in the holomorphic context without any modification. As a consequence we give another proof of the following theorem: a holomorphic Poisson manifold is integrable if, and only if, its real (or imaginary) part is integrable as a real Poisson manifold.

26 pages, second part of arXiv:0707.4253 which was split into two, v2: example 3.19 and section 3.7 added

References in corpus (1)

• Poisson Quasi-Nijenhuis Manifolds

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• Lie-Nijenhuis bialgebroids
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• Multiplicative Connections and Their Lie Theory
• Integrating Nijenhuis Structures
• Hyperkahler metrics near Lagrangian submanifolds and symplectic groupoids