منابع مشابه
Reduction of Poisson Manifolds
Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.
متن کاملQuantizing Poisson Manifolds
This paper extends Kontsevich’s ideas on quantizing Poisson manifolds. A new differential is added to the Hodge decomposition of the Hochschild complex, so that it becomes a bicomplex, even more similar to the classical Hodge theory for complex manifolds. These notes grew out of the author’s attempt to understand Kontsevich’s ideas [Kon95a] on quantizing Poisson manifolds. We introduce a new di...
متن کاملCoisotropic embeddings in Poisson manifolds
We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, wh...
متن کاملSymplectic Groupoids and Poisson Manifolds
0. Introduction. A symplectic groupoid is a manifold T with a partially defined multiplication (satisfying certain axioms) and a compatible symplectic structure. The identity elements in T turn out to form a Poisson manifold To? and the correspondence between symplectic groupoids and Poisson manifolds is a natural extension of the one between Lie groups and Lie algebras. As with Lie groups, und...
متن کاملDeformations of Holomorphic Poisson Manifolds
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters—an elliptic curve and a translation on ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2019
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2018.10.017