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＜電子ブック＞
Poisson Structures / by Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 347)

版	1st ed. 2013.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XXIV, 464 p : online resource
著者標目	*Laurent-Gengoux, Camille author Pichereau, Anne author Vanhaecke, Pol author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Geometry, Differential LCSH:Topological groups LCSH:Lie groups LCSH:Nonassociative rings FREE:Analysis FREE:Differential Geometry FREE:Topological Groups and Lie Groups FREE:Non-associative Rings and Algebras
一般注記	Part I Theoretical Background:1.Poisson Structures: Basic Definitions -- 2.Poisson Structures: Basic Constructions -- 3.Multi-Derivations and Kähler 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.R-Brackets and r-Brackets -- 11.Poisson–Lie 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.   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 HTTP:URL=https://doi.org/10.1007/978-3-642-31090-4

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