Geodeics on the coset spaces as a dynamical realization of l-conformal Galilei algebra

Abstract

In recent years nonrelativistic conformal Galilei algebras attracted considerable interest [2-7]. The conformal extension of the Galilei algebra is parameterized by a (half)integer parameter l [1]. A pecuilar feature of this algebra is that it involves acceleration generators along with the standard set of generators of Galilei algebra. Most of the examples of dynamical realizations of this algebra encouters with a problem of the precence of higher derivative terms or functional dependence of the acceleration generators. The main goal of this note is to construct metric on the coset space of l-conformal Galilei group and analyze corresponding geodesics equations. Considering geodesics equations as a dynamical realization, we show that it is free of the problems mentioned above.