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Contents
Contents
From Poisson to Quantum Geometry
Nicola Ciccoli
June 2006
Contents
Poisson Geometry
Poisson algebra
Poisson manifolds
The sharp map
The symplectic foliation
Schouten-Nijenhuis bracket
Lie-Poisson bracket
Schouten-Nijenhuis bracket
Schouten-Nijenhuis bracket computations
Lichnerowicz definition of the Schouten-Nijenhuis bracket
Jacobi condition and Schouten-Nijenhuis bracket
Compatible Poisson tensors
Koszul's formula
Poisson homology
Poisson maps
Poisson maps
Poisson submanifolds
Coinduced Poisson structures
Completeness
Poisson cohomology
Modular class
Computation for Poisson cohomology
Poisson homology
Poisson homology and modular class
Coisotropic submanifolds
Poisson Morita equivalence
Dirac structures
Poisson Lie groups
Poisson Lie groups
Lie bialgebras
Manin triples
Poisson actions
Poisson actions
Poisson homogeneous spaces
Dressing actions
Quantization
Introduction
Duality
Local, global, special quantizations
Real structures
Dictionary
Quantum subgroups
Quantum homogeneous spaces
Coisotropic creed
Bibliography
About this document ...
Pawel Witkowski 2006-06-26
