Nine-vectors, complex octonion/quaternion hypercomplex numbers, lie groups, and the ‘real’ world
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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.
KeywordsCovariance Wave Equation Multiplication Scheme Group Structure Equation Covariance
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