  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.
