  We show that the Drinfel'd double associated to the standard quantum
deformation $sl_\eta(2,R)$ is isomorphic to the (2+1)-dimensional AdS algebra
with the initial deformation parameter $\eta$ related to the cosmological
constant $\Lambda=-\eta^2$. This gives rise to a generalisation of a
non-commutative Minkowski spacetime that arises as a consequence of the quantum
double symmetry of (2+1) gravity to non-vanishing cosmological constant. The
properties of the AdS quantum double that generalises this symmetry to the case
$\Lambda\neq 0$ are sketched, and it is shown that the new non-commutative AdS
spacetime is a nonlinear $\Lambda$-deformation of the Minkowskian one.
