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Nine-vectors, complex octonion/quaternion hypercomplex numbers, lie groups, and the ‘real’ world

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Abstract

A “mental” multiplication scheme is given for the super hypercomplex numbers, which extend the 16-element Dirac algebra to 32 elements by appending the complex octonions. This extends the 5-vectors of relativity to 9-vectors. The problems with nonassociativity, for the group structures and wave equation covariance, are explored.

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Authors and Affiliations

  1. Department of Physics, Bucknell University, Lewisburg, Pennsylvania

    James D. Edmonds Jr.

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  1. James D. Edmonds Jr.
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Edmonds, J.D. Nine-vectors, complex octonion/quaternion hypercomplex numbers, lie groups, and the ‘real’ world. Found Phys 8, 303–311 (1978). https://doi.org/10.1007/BF00715215

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  • DOI: https://doi.org/10.1007/BF00715215

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