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A representation of the conformal Newton-Hooke algebra on a phase space of nparticles in arbitrary dimension which interact with one another via a genericconformal potential and experience a universal cosmological repulsion orattraction is constructed. The minimal N=2 superconformal extension of theNewton-Hooke algebra and its dynamical realization in many-body mechanics arestudied.

N=2 superconformal Newton-Hooke algebra and many-body mechanics