Curved momentum spaces from quantum groups with cosmological constant

by Iván Gutiérrez Sagredo (Università di Burgos)

Friday 26 Jan 2018, 17:00 → 17:30 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

Quantum symmetries are widely thought to introduce a nontrivial structure on momentum space. While the associated momentum space to the k-Poincaré symmetry was explicitly constructed some years ago, the case of non-vanishing cosmological constant remained an unsolved problem, because of the intertwining of momentum space and spacetime curvatures. In this seminar I will introduce the momentum spaces associated to the k-(A)dS deformation, using the language of Hopf algebras, both in (2+1) and (3+1) dimensions. This way we will see that the structure of these quantum deformations forces us to enlarge the momentum space to include 'hyperbolic' momenta associated to boost transformations. In order to give a geometrical interpretation of our results we consider the action of the dual Poisson-Lie group to the k-deformation on suitable spaces and we are able to describe the nontrivial momentum space as a submanifold of a higher dimensional de Sitter space or SO(4,4) quadric, depending on the concrete case.