Poisson Structures

  • Camille Laurent-Gengoux
  • Anne Pichereau
  • Pol Vanhaecke

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 347)

Table of contents

  1. Front Matter
    Pages I-XXIV
  2. Theoretical Background

    1. Front Matter
      Pages 1-1
    2. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 3-35
    3. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 37-61
    4. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 63-89
    5. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 91-112
    6. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 113-157
  3. Examples

    1. Front Matter
      Pages 159-159
    2. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 161-178
    3. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 179-203
    4. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 205-232
    5. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 233-267
    6. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 269-290
    7. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 291-325
  4. Applications

    1. Front Matter
      Pages 327-327
    2. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 329-351
    3. Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
      Pages 353-409
  5. Back Matter
    Pages 411-461

About this book

Introduction

Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization).
The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​

Keywords

17B63, 53D17, 17B80, 53D55, 17B62 Poisson Algebras Poisson geometry Poisson structures deformation quantization integrable systems

Authors and affiliations

  • Camille Laurent-Gengoux
    • 1
  • Anne Pichereau
    • 2
  • Pol Vanhaecke
    • 3
  1. 1.CNRS UMR 7122, Laboratoire de MathématiquesUniversité de LorraineMetzFrance
  2. 2.CNRS UMR 5208, Université Jean MonnetUniversité de LyonSaint EtienneFrance
  3. 3.CNRS UMR 7348, Lab. Mathématiques et ApplicationsUniversité de PoitiersFuturoscope ChasseneuilFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31090-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31089-8
  • Online ISBN 978-3-642-31090-4
  • Series Print ISSN 0072-7830
  • About this book