Abstract
First we calculate the product of two bivectors in vectorial spaceR(p, q) (p andq are integers such thatp+q=n).
Second we prove that this product is a quaternion forR(3, 0) and we generalize to finite number of bivectors.
Third we prove that this product is a biquaternion forR(1, 3) and we genaralize in the same way.
Fourth we prove that some complex quaternions can be connected with real Clifford algebra by choosing correctly the usual imaginary.
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Références
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Casanova, G. Produit de bivecteurs et quaternions complexes. AACA 8, 229–234 (1998). https://doi.org/10.1007/BF03043096
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DOI: https://doi.org/10.1007/BF03043096