In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in $R^{ 1,d-1}$ is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained trough a formal dimensional reduction from a free massless particle living in a $R^{ 2,d}$ space. Due this treatment it is possible to say that even DSR theories modify light cone structure in $R^{ 1,d-1}$, it could remains, in some cases, untouched in $R^{ 2,d}$.
Categories: gr-qc hep-th