Poisson Structures

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Laurent-Gengoux, Camille (Autor), Pichereau, Anne (Autor), Vanhaecke, Pol (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Colección:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 347
Temas:
Mathematical analysis.
Geometry, Differential.
Topological groups.
Lie groups.
Nonassociative rings.
Analysis.
Differential Geometry.
Topological Groups and Lie Groups.
Non-associative Rings and Algebras.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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