algebras and loops

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algebras and loops

The Cayley-Dickson process is used in connection with square array representations of the Cayley-Dickson algebras. This involves an array operation on square arrays distinct from matrix multiplication. The arrays give a convenient representation of the octonion divisionalgebra and a description of octonion multiplication. The connection between this descriptionof pure octonion multiplication and seven dimensional real space using products related to the commutator and associator of the octonions is extended to the other Cayley-Dickson algebras and the appropriate real vector space

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