Series: Grundlehren der mathematischen Wissenschaften, Vol. 347
Laurent-Gengoux, Camille, Pichereau, Anne, Vanhaecke, Pol
2013, XXIV, 464 p.
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Content Level » Research
Keywords » 17B63, 53D17, 17B80, 53D55, 17B62 - Poisson Algebras - Poisson geometry - Poisson structures - deformation quantization - integrable systems
Related subjects » Algebra - Analysis - Geometry & Topology
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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