The Galilean group in \(2+1\) space-times and its central extension

DOI10.1007/BF02099478zbMath0826.22020OpenAlexW2009644720MaRDI QIDQ1894865

Yanyan Li

Publication date: 26 July 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099478

zbMATH Keywords

Lie algebracentral extensionsuniversal covering groupGalilean groupangular momentum for systemsgroup of Galilean transformations

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Applications of differential geometry to physics (53Z05) Lie algebras of Lie groups (22E60)

Related Items (18)

Projective representations of the 1+1-dimensional Poincaré group ⋮ Three-dimensional Maxwellian extended Newtonian gravity and flat limit ⋮ Non-relativistic gravity theories in four spacetime dimensions ⋮ Three-dimensional exotic Newtonian gravity with cosmological constant ⋮ Faithful representations of the Galilean Lie algebra in two spatial dimensions ⋮ Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories ⋮ Modal-Hamiltonian interpretation of quantum mechanics and Casimir operators: the road toward quantum field theory ⋮ The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics ⋮ Comments on Galilean conformal field theories and their geometric realization ⋮ The symmetry groups of noncommutative quantum mechanics and coherent state quantization ⋮ A note on broken dilatation symmetry in planar noncommutative theory ⋮ Non-relativistic three-dimensional supergravity theories and semigroup expansion method ⋮ Quantum mechanics: Modal interpretation and Galilean transformations ⋮ Three-dimensional Maxwellian extended Bargmann supergravity ⋮ Quantum Theory as the Representation Theory of Symmetries ⋮ Remarks on the exotic central extension of the planar Galilei group ⋮ \((2+1)\)-dimensional models with a Chern-Simons-like term and noncommutative geometry ⋮ Symmetries of the Quantum State Space and Group Representations

Cites Work

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• Relativity groups in the presence of matter
• Quantum field theories of vortices and anyons
• On unitary ray representations of continuous groups
• SYMMETRIES AND QUANTIZATION: STRUCTURE OF THE STATE SPACE
• UNIVERSAL CENTRAL EXTENSIONS
• Galilei Group and Nonrelativistic Quantum Mechanics

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