Progress of Theoretical Physics
Supplement No.144 (2002) pp. 145-154
URL : http://ptp.ipap.jp/link?PTPS/144/145/
DOI : 10.1143/PTPS.144.145

Poisson Geometry with a 3-Form Background

Pavol Ševera^1,* and Alan Weinstein^2,**

We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these “twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.

^*Research supported by the European Postdoctoral Institute (EPDI).
E-mail: severa@sophia.dtp.fmph.uniba.sk
^**Research partially supported by NSF Grant DMS-99-71505.
E-mail: alanw@math.berkeley.edu

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1. Progress of Theoretical Physics Supplement No.144 (2002) pp. 26-37 :

   Poisson Vector Bundles, Contravariant Connections and Deformations

   Henrique Bursztyn

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