A (2+12+1) non-commutative Drinfel'd double spacetime with cosmological constant

We show that the Drinfel'd double associated to the standard quantum deformation slη(2,R)slη(2,R) is isomorphic to the (2+1)(2+1)-dimensional AdS algebra with the initial deformation parameter η   related to the cosmological constant Λ=−η2Λ=−η2. 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)(2+1) gravity to non-vanishing cosmological constant. The properties of the AdS quantum double that generalises this symmetry to the case Λ≠0Λ≠0 are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinear Λ-deformation of the Minkowskian one.