Extended Non Linear Conformal Symmetry and DSR Velocities on the Physical Surface

The relation between Conformal generators and Magueijo Smolin Deformed Special Relativity term, added to Lorentz boosts, is achieved. The same is performed for Fock Lorentz transformations. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a $d$ dimensional space, is isomorphic to 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 arises. Finally, because the relation between momenta and velocities is known, the problem of position space dynamics is solved.