Geodesic
Demonstration representation and tensor products of Clifford algebras
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 154-165.

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It is proved that the tensor product of any Clifford algebras is isomorphic to a single Clifford algebra over some commutative algebra. It is also proved that any complex or real Clifford algebra $\mathcal C\!\ell (p,q)$ can be represented as a tensor product of Clifford algebras of the second and first orders. A canonical form of such a representation is proposed. 
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N. G. Marchuk. Demonstration representation and tensor products of Clifford algebras. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 154-165. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a12/

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