The outer derivation of a complex Poisson manifold
Jean-Luc Brylinski, Gregg Zuckerman
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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