Poisson Geometry with a 3-Form Background | Zendy

Pavol Ševera | Zendy; Alan Weinstein | Zendy

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Poisson Geometry with a 3-Form Background

Author(s) -

Pavol Ševera,

Alan Weinstein

Publication year - 2001

Publication title -

progress of theoretical physics supplement

Language(s) - English

Resource type - Journals

ISSN - 0375-9687

DOI - 10.1143/ptps.144.145

Subject(s) - poisson distribution , symplectic geometry , poisson manifold , mathematics , geometry , poisson's ratio , quantization (signal processing) , pure mathematics , statistics , algorithm

We study a modification of Poisson geometry by a closed 3-form. Just as forordinary Poisson structures, these "twisted" Poisson structures areconveniently described as Dirac structures in suitable Courant algebroids. Theadditive group of 2-forms acts on twisted Poisson structures and permits themto be seen as glued from ordinary Poisson structures defined on local patches.We conclude with remarks on deformation quantization and twisted symplecticgroupoids.

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