**Contemporary Mathematics**

Volume: 450;
2008;
311 pp;
Softcover

MSC: Primary 53; 19; 58; 81; 14; 22; 47;

Print ISBN: 978-0-8218-4423-6

Product Code: CONM/450

List Price: $103.00

AMS Member Price: $82.40

MAA Member Price: $92.70

**Electronic ISBN: 978-0-8218-8129-3
Product Code: CONM/450.E**

List Price: $97.00

AMS Member Price: $77.60

MAA Member Price: $87.30

# Poisson Geometry in Mathematics and Physics

Share this page *Edited by *
*Giuseppe Dito; Jiang-Hua Lu; Yoshiaki Maeda; Alan Weinstein*

This volume is a collection of articles by speakers at the conference “Poisson 2006: Poisson Geometry in Mathematics and Physics”, which was held June 5–9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring together mathematicians and mathematical physicists who work in diverse areas but have common interests in Poisson geometry. The program for Poisson 2006 was remarkable for the overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction. The articles represent current research in Poisson geometry and should be valuable to anyone interested in Poisson geometry, symplectic geometry, and mathematical physics. This volume also contains lectures by the principal speakers of the three-day school held at Keio University that preceded Poisson 2006.

#### Readership

Graduate students and research mathematicians interested in Symplectic and Poisson geometry, deformation quantization, and mathematical physics.

# Table of Contents

## Poisson Geometry in Mathematics and Physics

- Contents v6 free
- Foreword vii8 free
- List of Participants ix10 free
- Quantized Anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces 116 free
- Group-like objects in Poisson geometry and algebra 2540
- Poisson fibrations and fibered symplectic groupoids 4156
- Generalized Kähler and hyper-Kähler quotients 6176
- Deformation quantization and reduction 7994
- Examples of higher order stable singularities of Poisson structures 103118
- Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations 113128
- Orbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces 127142
- Deformation of graded Poisson (Batalin-Vilkovisky) structures 147162
- Deformation quantization of a Kähler-Poisson structure vanishing on a Levi nondegenerate hypersurface 163178
- A note on Poisson homogeneous spaces 173188
- Lectures on pure spinors and moment maps 199214
- Lectures on PROPs, Poisson geometry and deformation quantization 223238
- Deformation quantization modules on complex symplectic manifolds 259274
- Non-commutative quasi-Hamiltonian spaces 273288
- 1. Introduction 273288
- 2. Preliminaries 274289
- 3. Generalities about bimodules 279294
- 4. Quasi-Poisson and quasi-Hamiltonian G-spaces 283298
- 5. Hamiltonian double quasi-Poisson algebras 285300
- 6. Quasi-bisymplectic algebras 287302
- 7. Compatibility 288303
- 8. More general base rings and quivers 295310
- References 299314

- Locally noncommutative space-times 301316