Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes

Abstract

Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z=2/N with N=1,2,.... Their underlying group structure and matrix representation are constructed (up to a covering) by means of the Veronese map of degree N. Suitable quotients of the conformal Galilei groups provide us with Newton-Hooke nonrelativistic spacetimes with a quantized reduced negative cosmological constant λ=-N.

LaTeX, 31 pages. Sections 3 and 5 reorganized. Conclusion expanded. New references added

References in corpus (11)

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• Galilean Isometries
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Cited by in corpus (64)

• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• `Stringy' Newton-Cartan Gravity
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Cosmological aspects of the Eisenhart-Duval lift
• Dynamical realizations of l-conformal Newton-Hooke group
• Nonrelativistic conformal groups and their dynamical realizations
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• On dynamical realizations of l-conformal Galilei groups
• On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
• Scaling and conformal symmetries for plane gravitational waves
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Conformal and projective symmetries in Newtonian cosmology
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Ricci-flat spacetimes with l-conformal Galilei symmetry
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• 2d Galilean Field Theories with Anisotropic Scaling
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Three-dimensional exotic Newtonian gravity with cosmological constant
• Kohn's theorem and Newton-Hooke symmetry for Hill's equations
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Schrödinger Manifolds
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• The odd-order Pais-Uhlenbeck oscillator
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Three-dimensional non-relativistic supergravity and torsion
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Generalized Relativistic Kinematics
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Unitary representations of N-conformal Galilei group
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras
• Extended Kinematical 3D Gravity Theories
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Conformal mechanics
• New realizations of N=2 l-conformal Newton-Hooke superalgebra
• Non-relativistic gravity theories in four spacetime dimensions
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• On Casimir Operators of Conformal Galilei Algebras
• Higher-derivative generalization of conformal mechanics
• Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator
• Remarks on higher Schwarzians
• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Perfect fluid dynamics with conformal Newton-Hooke symmetries
• Covariant Formulation of the Newton-Hooke Particle and its Canonical Analysis
• Generalized conformal pseudo-Galilean algebras and their Casimir operators
• Generalized Massive Gravity and Galilean Conformal Algebra in two dimensions
• Wess-Zumino-Witten Model for Galilean Conformal Algebra
• Casimir operators of centrally extended l-conformal Galilei algebra
• Three-dimensional non-relativistic Hietarinta supergravity
• Conformal symmetry in damped Pais-Uhlenbeck oscillator
• Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry
• Nonlinear realizations and the orbit method
• Space-time Schrödinger symmetries of a post-Galilean particle
• Remarks on Galilean electromagnetism