The outer derivation of a complex Poisson manifold

1998/02/03 by Jean-Luc Brylinski, Brylinski, Jean-Luc, Gregg J. Zuckerman +2
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Advanced Topics in Algebra #math.DG

paper · pdf · doi:10.48550/arxiv.math/9802014

plain tex, 9 pages

arxiv created 1998/02/03 · arxiv updated 2009/11/30

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.

Cited by

• Poisson harmonic forms, Kostant harmonic forms, and the S¹-equivariant cohomology of K/T
• The modular automorphism group of a Poisson manifold

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