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

Understand

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 \lambda=-N.