  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
$R^{2,d}$.
