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00925njm 22002777a 4500 dc Ballesteros Castañeda, Ángel author Gubitosi, G. . author Gutiérrez Sagredo, Iván author Herranz Zorrilla, Francisco José author 2017-10 We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanish-ing cosmological constant . In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 +1)and (2 +1)dimensions is explicitly constructed as a dual Poisson–Lie group manifold parametrized by . Such momentum space includes both the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit →0, where hyperbolic momenta decouple from translational mo-menta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 +1)-dimensional ones. 0370-2693 http://hdl.handle.net/10259/4719 10.1016/j.physletb.2017.08.008 Curved momentum spaces from quantum groups with cosmological constant