Uniqueness of 4- and 8-Dimensional Spaces

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Abstract
Among rotation groups Rn, the cases n = 4 and 8 are unique in having two inequivalent n × n representations. Mathematically this is related to the uniqueness of quaternions and octonions; physically these groups seem to underlie the real and charge‐space symmetries of elementary particles. An attempt is made to interpret this fact by assuming a lack of inherent geometrical preference between Fermi‐Dirac and Bose‐Einstein statistics. Corollaries are the identity of real and charge‐space statistics and the complete disjointness of real and charge‐space coordinates.

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