Extended conformal group and DSR velocities on the physical surface

The relation between conformal generators and Magueijo-Smolin Doubly Special Relativity term, is achieved. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a d-dimensional space, is isomorphic to the one living in a d + 2 space with pure Lorentz invariance and to a particle living in a AdS_d+1 space. To accomplish these identifications, the conformal group is extended and a nonlinear algebra is obtained. Finally, because the relation between momenta and velocities is known through the dimensional reduction procedure, the problem of position space dynamics is solved.