Coisotropic embeddings in Poisson manifolds
Coisotropic embeddings in Poisson manifolds
复制标题
泊松流形中的各向同性嵌入
DOI：
10.1090/s0002-9947-09-04667-4
复制
发表时间：
2006
影响因子：
1.3
通讯作者：
M. Zambon
中科院分区：
文献类型：
--
作者：
A. Cattaneo;M. Zambon
我们考虑了两种各向同性嵌入的存在性和唯一性，并推导了某些基本函数的泊松代数的变形量化的存在性。首先，我们表明，泊松流形的任何子流形满足一定的常等级条件（卡尔沃和法尔切托（2004）已经考虑过），各向同性地位于一些较大的共辛子流形内，该子流形自然地具有泊松结构。然后我们给出了狄拉克流形可以各向同性嵌入到泊松流形中的条件，扩展了戈泰的经典定理。
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, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.