The Magueijo-Smolin Group in Doubly-Special Relativity is Linear in Five Dimensions

Magueijo and Smolin have introduced a modification of the Lorentz group for the momentum-space transformations in Doubly-Special Relativity. As presented the group is non-linear, but we show that it is a group of fraction-linear transformations in 4 dimensional real projective space. We pass to the associated 5 dimensional linear space and identify the subgroup as a conjugate of the ordinary Lorentz group, giving the conjugating matrix. Taking the dual of the 5-space, we identify a subgroup as the Lorentz transformations about a point different to the origin.