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The outer derivation of a complex Poisson manifold

Jean-Luc Brylinski·Gregg Zuckerman
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Abstract

We introduce a canonical outer vector field on a Poisson manifold, also due independently to A. Weinstein. We view it as a global section of the sheaf of Poisson vector fields modulo the subsheaf of hamiltonian vector fields. We study this outer derivation mostly in the case of holomorphic Poisson manifolds.

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Jean-Luc Brylinski, Gregg Zuckerman. 1998-02-03. The outer derivation of a complex Poisson manifold. https://arxiv.org/abs/math/9802014

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