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

摘要

We show that the Drinfel'd double associated to the standard quantum deformationslη(2,R)is isomorphic to the(2+1)-dimensional AdS algebra with the initial deformation parameterηrelated to the cosmological constantΛ=?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)gravity to non-vanishing cosmological constant. The properties of the AdS quantum double that generalises this symmetry to the caseΛ≠0are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinearΛ-deformation of the Minkowskian one.