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 Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 154–165 (Mi tm3635)

Demonstration representation and tensor products of Clifford algebras

N. G. Marchuk

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: 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.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.1134/S0371968515030139

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 143–154

Bibliographic databases:

Document Type: Article
UDC: 512.81

Citation: N. G. Marchuk, “Demonstration representation and tensor products of Clifford algebras”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 154–165; Proc. Steklov Inst. Math., 290:1 (2015), 143–154

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3635
• https://doi.org/10.1134/S0371968515030139
• http://mi.mathnet.ru/eng/tm/v290/p154

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409
2. B. O. Volkov, “Stochastic Levy differential operators and Yang–Mills equations”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:2 (2017), 1750008
3. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108
4. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271
5. N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27
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