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,\dots. 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 \lambda=-N.
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Contributor : Christian Duval <>
Submitted on : Monday, July 4, 2011 - 11:11:12 AM
Last modification on : Tuesday, September 24, 2019 - 1:17:40 AM
Long-term archiving on : Wednesday, October 5, 2011 - 2:22:01 AM

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Christian Duval, Peter Horvathy. Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2011, 44, 335203 (21pp). ⟨10.1088/1751-8113/44/33/335203⟩. ⟨hal-00583704v3⟩

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