Poisson structures
 Author/Creator
 LaurentGengoux, Camille.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer Verlag, c2013.
 Physical description
 xxiv, 461 p. : ill ; 24 cm.
 Series
 Grundlehren der mathematischen Wissenschaften ; 347.
Access
Contributors
 Contributor
 Pichereau, Anne.
 Vanhaecke, Pol, 1963
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Part I Theoretical Background:1.Poisson Structures: Basic Definitions. 2.Poisson Structures: Basic Constructions. 3.MultiDerivations and Kahler Forms. 4.Poisson (Co)Homology. 5.Reduction. Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds. 7.Linear Poisson Structures and Lie Algebras. 8.Higher Degree Poisson Structures. 9.Poisson Structures in Dimensions Two and Three. 10.RBrackets and rBrackets. 11.PoissonLie Groups. Part III Applications:12.Liouville Integrable Systems. 13.Deformation Quantization. A Multilinear Algebra. B Real and Complex Differential Geometry. References. Index. List of Notations.
 (source: Nielsen Book Data)
 Publisher's 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Camille LaurentGengoux, Anne Pichereau, Pol Vanhaecke.
 Series
 Grundlehren der mathematischen Wissenschaften, a series of comprehensive studies in mathematics, 00727830 ; 347
 Note
 Also issued online.
 ISBN
 9783642310898
 3642310893