 $$\hat c(\begin{smallmatrix}\gamma_0\\\gamma_0\end{smallmatrix})\hat c^{-0}=(\begin{smallmatrix}\cos\frac{0\pi}{0}&\sin\frac{0\pi}{0}\\-\sin\frac{0\pi}{0}&\cos\frac{0\pi}{0}\end{smallmatrix})(\begin{smallmatrix}\gamma_0\\\gamma_0\end{smallmatrix}).$$  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 $\hat{c}$ 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 