$\mathcal E$ of Quantum Spacetime can be associated to the above relations, by a procedure [@DF; @BDMP] which applies to more general cases.

Assuming that the $q_\lambda,  Q_{\mu \nu}$ are selfadjoint operators and that the $Q_{\mu \nu}$ commute $strongly$ with one another and with the $q_\lambda$, the relations above can be seen as a bundle of Lie Algebra relations based on the joint spectrum of the $Q_{\mu \nu}$.

*Regular representations* are described by representations of the C\* group algebra of the unique simply connected Lie group associated to the corresponding Lie algebra, with the condition that $I$ is not an independent generator but is represented by the unit operator. They obey the Weyl relations $$\label{eq:weyl_rels} 
e^{ih_\mu q^\mu}e^{ik_\nu q^\nu}=e^{-\frac i2h_\mu Q^{\mu\nu} k_\nu}e^{i(h+k)_\mu q^\mu},\quad h,k\in\mathbb R^4.$$

The C\* algebra of Quantum Spacetime is the C\* algebra of a continuous field of group C\* algebras based on the spectrum of a commutative C\* algebra.

In our case, that spectrum - the joint spectrum of the $Q_{\mu \nu}$ - is the manifold $\Sigma$ of the real valued antisymmetric 2-tensors fulfilling the same relations as the $Q_{\mu \nu}$ do: a homogeneous space of the proper orthochronous Lorentz group, identified with the coset space of $SL(2,\bC)$ 