Abstract
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 R1,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 through a formal dimensional reduction from a free massless particle living in a R2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R1,d-1, it could remains, in some cases, untouched in R2,d.
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