GEOMETRIC QUANTIZATION OF HAMILTONIAN ACTIONS OF LIE ALGEBROIDS AND LIE GROUPOIDS

DOI10.1142/S0219887807002077zbMath1140.22002arXivmath/0604027OpenAlexW2143346685MaRDI QIDQ3502873

Rogier Bos

Publication date: 20 May 2008

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604027

zbMATH Keywords

Lie algebroidsLie groupoidsrepresentation theorygeometric quantizationorbit methodhamiltonian action

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Foliations in differential topology; geometric theory (57R30) Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05) Geometric quantization (53D50)

Related Items (7)

Quantisation commutes with reduction at discrete series representations of semisimple groups ⋮ Linking Lie groupoid representations and representations of infinite-dimensional Lie groups ⋮ Hamiltonian Lie algebroids ⋮ Unnamed Item ⋮ The Lie algebroid Poisson sigma model ⋮ GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS ⋮ Equivariant differential characters and symplectic reduction

Cites Work

• Unnamed Item
• Moments and reduction for symplectic groupoids
• An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg
• Geometric quantization and multiplicities of group representations
• Reduction of symplectic manifolds with symmetry
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Singular reduction and quantization
• The Baum-Connes conjecture for amenable foliations
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
• Integrability of Lie brackets
• On integrability of infinitesimal actions
• Symplectic groupoids and Poisson manifolds
• Transverse measures, the modular class and a cohomology pairing for Lie algebroids
• Localization of the Riemann-Roch character

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