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Ballesteros Castañeda, Ángel Gubitosi, G. . Gutiérrez Sagredo, Iván Herranz Zorrilla, Francisco José 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. 2018-02-01 2018-02-01 2017-10 info:eu-repo/semantics/article 0370-2693 http://hdl.handle.net/10259/4719 10.1016/j.physletb.2017.08.008 eng Physics Letters B. 2017, V. 773, p. 47-53 https://doi.org/10.1016/j.physletb.2017.08.008 info:eu-repo/grantAgreement/MINECO/MTM2013-43820-P info:eu-repo/grantAgreement/MINECO/MTM2016-79639-P info:eu-repo/grantAgreement/JCyL/BU278U14 info:eu-repo/grantAgreement/JCyL/VA057U16 info:eu-repo/grantAgreement/UE/COST-MP1405 info:eu-repo/grantAgreement/JohnTempletonFoundation/47633 http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Attribution 4.0 International Elsevier