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

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.

preprint2011arXivOpen access
Christian DuvalPeter Horvathy
math-phmath.MPhep-th
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Christian DuvalPeter Horvathy

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