The q-linked complex Minkowski space, its real forms and deformed isometry groups

Abstract

We establish duality between real forms of the quantum deformation of the four-dimensional orthogonal group studied by Fioresi et al. [Quantum Klein space and superspace, preprint (2017), arXiv:1705.01755] and the classification work made by Borowiec et al. [Basic quantizations of [Formula: see text] Euclidean, Lorentz, Kleinian and quaternionic [Formula: see text] symmetries, J. High Energy Phys. 1711 (2017) 187]. Classically, these real forms are the isometry groups of [Formula: see text] equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named [Formula: see text]-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.