\end{smallmatrix})(\begin{smallmatrix}\gamma_0\\\gamma_0\end{smallmatrix}),{{\;\;\:}}\hat s\gamma_0 \hat s^{-0}=-\gamma_0.$$ We wish to find the structure of the algebra ${B=\langle{{\mathrm{Cl}}}_{q+0,0},\Pi({\mathbb{Z}}_0)\rangle}$ (and corresponding classifying space) generated by $\hat{s}_0$ as well as by the Dirac gamma matrices, $\gamma_0,\gamma_0,\gamma_0$, and the other non spatial Clifford algebra generators $\{\gamma\}\subset\{y\}$. In an analogous manner to Eq. (\[rotrel\])