  The Poincar\'e sector of a recently deformed conformal algebra is proposed to
describe, after the identification of the deformation parameter with the Planck
length, the symmetries of a new relativistic theory with two
observer-independent scales (or DSR theory). Also a new non-commutative
space-time is proposed. It is found that momentum space exhibits the same
features of the DSR proposals preserving Lorentz invariance in a deformed way.
The space-time sector is a generalization of the well known non-commutative
$\kappa$-Minkowski space-time which however does not preserve Lorentz
invariance, not even in the deformed sense. It is shown that this behavior
could be expected in some attempts to construct DSR theories starting from the
Poincar\'e sector of a deformed symmetry larger than Poincar\'e symmetry,
unless one takes a variable Planck length. It is also shown that the formalism
can be useful in analyzing the role of quantum deformations in the ``AdS-CFT
correspondence".
