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\begin{document}$${\mathcal{C}\ell_{p,q}}$$\end{document} the Clifford algebra on the real vector space \documentclass[12pt]{minimal}
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\begin{document}$${\mathbb{R}^{p,q}}$$\end{document}. This paper gives a unified tensor product expression of \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{C}\ell_{p,q}}$$\end{document} by using the center of \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{C}\ell_{p,q}}$$\end{document}. The main result states that for nonnegative integers p, q, \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{C}\ell_{p,q} \simeq \otimes^{\kappa-\delta}\mathcal{C}_{1,1} \otimes Cen(\mathcal{C}\ell_{p,q}) \otimes^{\delta} \mathcal{C}\ell_{0,2},}$$\end{document} where \documentclass[12pt]{minimal}
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\begin{document}$${p + q \equiv \varepsilon}$$\end{document} mod 2, \documentclass[12pt]{minimal}
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\begin{document}$${\kappa = ((p + q) - \varepsilon)/2, p - |q - \varepsilon| \equiv i}$$\end{document} mod 8 and \documentclass[12pt]{minimal}
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\begin{document}$${\delta = \lfloor i / 4 \rfloor}$$\end{document}.
