Poisson structures by Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke

Format:

Book

Author/Creator:

Laurent-Gengoux, Camille

Contributor:

Pichereau, Anne

Vanhaecke, Pol, 1963-

Series:

Grundlehren der mathematischen Wissenschaften 347

Grundlehren der mathematischen Wissenschaften 0072-7830 347

Language:

English

Subjects (All):

Poisson manifolds.

Poisson algebras.

Poisson distribution.

Poisson Distribution.

Medical Subjects:

Poisson Distribution.

Physical Description:

1 online resource

Place of Publication:

Berlin New York Springer ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

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

Contents:

Part 1. Theoretical Background Poisson Structures: Basic Definitions Poisson Structures: Basic Constructions Multi-Derivations and Kähler Forms Poisson (Co)Homology Reduction

Part 2. Examples Constant Poisson Structures, Regular and Symplectic Manifolds Linear Poisson Structures and Lie Algebras Higher Degree Poisson Structures Poisson Structures in Dimensions Two and Three

R-Brackets and r-Brackets Poisson-Lie Groups

Part 3. Applications Liouville Integrable Systems Deformation Quantization

Notes:

Includes bibliographical references and index

Other Format:

Print version Laurent-Gengoux, Camille. Poisson structures

ISBN:

9783642310904

3642310907

1283630842

9781283630849

9786613943293

6613943290

OCLC:

808814491

Access Restriction:

Restricted for use by site license