Quantum groups and noncommutative spacetimes with cosmological constant

8th International Workshop DICE2016: Spacetime - Matter - Quantum Mechanics 12–16 September 2016, Castiglioncello, ItalyNoncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter z is related to a Planck scale, and the cosmological constant Λ plays the role of a second deformation parameter of geometric nature, whose limit Λ → 0 provides the corresponding noncommutative Minkowski spacetimes.Ministerio de Econom´ıa y Competitividad (MINECO, Spain) under grants MTM2013-43820-P and MTM2016-79639-P, by Junta de Castilla y Le´on (Spain) under grants BU278U14 and VA057U16 and by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST