DEFORMATION QUANTIZATION OF CERTAIN NONLINEAR POISSON STRUCTURES

DOI10.1142/S0129167X98000269zbMath0916.46052arXivmath/9802034OpenAlexW2099921817MaRDI QIDQ4214630

Byung-Jay Kahng

Publication date: 1 November 1998

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9802034

zbMATH Keywords

deformation quantizationsLie brackettwisted group \(C^*\)-algebrasnonlinear Poisson bracketsnon-compact quantum groupscocycle perturbationsdual space of a Lie algebraLie algebra cocycleslinear Poisson bracket

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (2)

A \((2n+1)\)-dimensional quantum group constructed from a skew-symmetric matrix ⋮ Quantizations of some Poisson--Lie groups: the bicrossed product construction

Cites Work

• The local structure of Poisson manifolds
• Continuous fields of \(C^*\)-algebras coming from group cocycles and actions
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Quantum deformations of the Heisenberg group obtained by geometric quantization
• Déformation du crochet de Poisson sur une variété symplectique
• Deformation theory and quantization. I: Deformations of symplectic structures
• Die Eindeutigkeit der Schrödingerschen Operatoren
• Deformation quantization of Heisenberg manifolds
• Twisted crossed products of \(C^*\)-algebras. II
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures
• Twisted crossed products of C*-algebras
• On the Structure of Twisted Group C ∗ -Algebras
• AFFINE POISSON STRUCTURES

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