  The essential features of a quantum group deformation of classical symmetries
of General Relativity in the case with non-vanishing cosmological constant
$\Lambda$ are presented. We fully describe (anti-)de Sitter non-commutative
spacetimes and curved momentum spaces in (1+1) and (2+1) dimensions arising
from the $\kappa$-deformed quantum group symmetries. These non-commutative
spacetimes are introduced semiclassically by means of a canonical Poisson
structure, the Sklyanin bracket, depending on the classical $r$-matrix defining
the $\kappa$-deformation, while curved momentum spaces are defined as orbits
generated by the $\kappa$-dual of the Hopf algebra of quantum symmetries.
Throughout this construction we use kinematical coordinates, in terms of which
the physical interpretation becomes more transparent, and the cosmological
constant $\Lambda$ is included as an explicit parameter whose $\Lambda
\rightarrow 0$ limit provides the Minkowskian case. The generalization of these
results to the physically relevant (3+1)-dimensional deformation is also
commented.
