  We present two different quantum deformations for the (anti)de Sitter
algebras and groups. The former is a non-standard (triangular) deformation of
SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime,
while the latter is a standard (quasitriangular) deformation of both SO(2,2)
and SO(3,1) expressed as the kinematical groups of the (2+1)D anti-de Sitter
and de Sitter spacetimes, respectively. The Hopf structure of the quantum
algebra and a study of the dual quantum group are presented for each
deformation. These results enable us to propose new non-commutative spacetimes
that can be interpreted as generalizations of the kappa-Minkowski space, either
by considering a variable deformation parameter (depending on the boost
coordinates) in the conformal deformation, or by introducing an explicit
curvature/cosmological constant in the kinematical one; kappa-Minkowski turns
out to be the common first-order structure for all of these quantum spaces.
Some properties provided by these deformations, such as dimensions of the
deformation parameter (related with the Planck length), space isotropy,
deformed boost transformations, etc., are also commented.
