The outer derivation of a complex Poisson manifold

Authors:
  • JBJ. L Brylinski
    J. L Brylinski
  • GZG Zuckerman
    G Zuckerman
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Abstract
We introduce the canonical outer derivation (or vector field) on a Poisson manifold. This is a Poisson vector field well-defined modulo hamiltonian vector fields.We study this outer derivation by geometric and sheaf-theoretic methods, mostly for holomorphic Poisson manifolds.