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Demonstration representation and tensor products of Clifford algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2015_290_a12,
     author = {N. G. Marchuk},
     title = {Demonstration representation and tensor products of {Clifford} algebras},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {154--165},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a12/}
}
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N. G. Marchuk. Demonstration representation and tensor products of Clifford algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 154-165. http://geodesic.mathdoc.fr/item/TM_2015_290_a12/