Acceleration-extended Galilean symmetries with central charges and their dynamical realizations

We add to Galilean symmetries the transformations describing constant accelerations. The corresponding extended Galilean algebra allows, in any dimension D=d+1, the introduction of one central charge c while in D=2+1 we can have three such charges: c,θ and θ′. We present nonrelativistic classical mechanics models, with higher order time derivatives and show that they give dynamical realizations of our algebras. The presence of central charge c requires the acceleration square Lagrangian term. We show that the general Lagrangian with three central charges can be reinterpreted as describing an exotic planar particle coupled to a dynamical electric and a constant magnetic field.