Poisson Structures

• Κύριοι συγγραφείς: Laurent-Gengoux, Camille (Συγγραφέας), Pichereau, Anne (Συγγραφέας), Vanhaecke, Pol (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Σειρά: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 347
• Θέματα: Mathematics.; Nonassociative rings.; Rings (Algebra).; Topological groups.; Lie groups.; Mathematical analysis.; Analysis (Mathematics).; Differential geometry.; Analysis.; Differential Geometry.; Topological Groups, Lie Groups.; Non-associative Rings and Algebras.

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 a...

Πίνακας περιεχομένων:

• 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.  .