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130626 ||| eng |
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|a 9783642310904
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|a Laurent-Gengoux, Camille
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| 245 |
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|a Poisson Structures
|h Elektronische Ressource
|c by Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke
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| 250 |
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|a 1st ed. 2013
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2013, 2013
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| 300 |
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|a XXIV, 464 p
|b online resource
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|a 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.
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Topological Groups and Lie Groups
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| 653 |
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|a Lie groups
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| 653 |
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|a Topological groups
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| 653 |
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|a Nonassociative rings
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| 653 |
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|a Analysis
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Non-associative Rings and Algebras
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| 700 |
1 |
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|a Pichereau, Anne
|e [author]
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| 700 |
1 |
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|a Vanhaecke, Pol
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| 028 |
5 |
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|a 10.1007/978-3-642-31090-4
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-642-31090-4?nosfx=y
|x Verlag
|3 Volltext
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|a 515
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|a 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
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