Quantum Klein Space and Superspace

Abstract

We give an algebraic quantization, in the sense of quantum groups, of the complex Minkowski space, and we examine the real forms corresponding to the signatures $(3,1)$, $(2,2)$, $(4,0)$, constructing the corresponding quantum metrics and providing an explicit presentation of the quantized coordinate algebras. In particular, we focus on the Kleinian signature $(2,2)$. The quantizations of the complex and real spaces come together with a coaction of the quantizations of the respective symmetry groups. We also extend such quantizations to the $\mathcal{N}=1$ supersetting.

References in corpus (8)

• Double Field Theory
• Symmetries of quantum space-time in 3 dimensions
• The Minkowski and conformal superspaces
• Pseudo-Riemannian VSI spaces II
• Quantum deformations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries in unified $\mathfrak{o}(4;\mathbb{C})$ setting -- Addendum
• SO*(2N) coherent states for loop quantum gravity
• Pseudo-Riemannian VSI spaces
• Quadratic deformation of Minkowski space

Cited by in corpus (2)

• The Segre embedding of the quantum conformal superspace
• The $q$-linked complex Minkowski space, its real forms and deformed isometry groups