Semidirect products and the Pukanszky condition

DOI10.1016/S0393-0440(97)00028-4zbMath0932.22011arXivdg-ga/9705005WikidataQ127147675 ScholiaQ127147675MaRDI QIDQ1299136

P. Baguis

Publication date: 8 March 2000

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9705005

zbMATH Keywords

coadjoint orbitsGalilei groupspecial Euclidean groupsymplectic inductionBargmann groupnonrelativistic particle dynamics

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (15)

Manifestly covariant worldline actions from coadjoint orbits. I: Generalities and vectorial descriptions ⋮ Matrix quantization of gravitational edge modes ⋮ Geometric actions for three-dimensional gravity ⋮ Another proof for the continuity of the Lipsman mapping ⋮ A bijection between the adjoint and coadjoint orbits of a semidirect product ⋮ Linear dynamical systems of nilpotent Lie groups ⋮ Gravitational edge modes, coadjoint orbits, and hydrodynamics ⋮ Non-relativistic limits and three-dimensional coadjoint Poincaré gravity ⋮ Notes on the BMS group in three dimensions. II: Coadjoint representation ⋮ The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements ⋮ Weyl quantization for semidirect products ⋮ Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups ⋮ Symplectic reduction for semidirect products and central extensions ⋮ Induction of Hamiltonian Poisson actions ⋮ Uncertainty principles for magnetic structures on certain coadjoint orbits

Cites Work

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• Induced representations and induced Hamiltonian actions
• Pukanszky's condition and symplectic induction
• Geometric quantization and quantum mechanics
• A universal phase space for particles in Yang-Mills fields
• Rieffel induction as generalized quantum Marsden-Weinstein reduction
• Semidirect Products and Reduction in Mechanics
• Representations of a semi-direct product by quantization
• Hamiltonian group actions and dynamical systems of calogero type
• Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field
• On the Theory of Exponential Groups

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