Abstract
A construction of the Clifford algebra CI(E) associated with an euclidean space E is proposed. It is based on the Clifford products aA and Aa of a vector a of E and all element A of the Grassmann algebra of E, which include the inner product of E, these products being taken as definitions. One deduces then that a(Ab) = (aA)b, and so that CI(E) is an associative algebra. Its remarkable relation with the group O(E) is emphasized.
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References
D. Hestenes, Space–Time Algebra. (Gordon and Breach, New-York, 1966)
R. Boudet, in Clifford algebras and their applications in mathematical physics, ed. by A. Micali, R. Boudet and J. Helmstetter (Kluwer, Dordrecht, 1992), p. 343
R. Boudet, Ann. Fond. L. de Broglie 13, 105 (1988)
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© 2011 Springer-Verlag Berlin Heidelberg
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Boudet, R. (2011). Real Algebras Associated with an Euclidean Space. In: Quantum Mechanics in the Geometry of Space-Time. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19199-2_14
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DOI: https://doi.org/10.1007/978-3-642-19199-2_14
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