Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 066, 20 pages      arXiv:1705.01755      https://doi.org/10.3842/SIGMA.2018.066

Quantum Klein Space and Superspace

Rita Fioresi a, Emanuele Latini ab and Alessio Marrani c
a) Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italy
b) INFN, Sez. di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
c) Museo Storico della Fisica e Centro Studi e Ricerche ''Enrico Fermi'', Via Panisperna 89A, I-00184, Roma, Italy

Received February 23, 2018, in final form June 15, 2018; Published online June 28, 2018

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.

Key words: quantum groups; supersymmetry.

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