COISOTROPIC EMBEDDINGS IN POISSON MANIFOLDS

被引：14

作者：

Cattaneo, A. S. ^{[1
]}

Zambon, M. ^{[2
]}

机构：

[1] Univ Zurich Irchel, Inst Math, CH-8057 Zurich, Switzerland

[2] Univ Porto, Dept Matemat Pura, P-4169007 Oporto, Portugal

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 07期

关键词：

SIGMA MODELS; SUBMANIFOLDS; BRACKETS; BRANES;

D O I：

10.1090/S0002-9947-09-04667-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：3721 / 3746

页数：26