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Added 2018.10.30: The Dixon Algebra. No longer can one count on the fingers of one hand the number of times T = C ⊗ H ⊗ O has been refered to in the literature (popular and technical) as the Dixon Algebra. Still, as I recently discovered, and am in agreement with, this is not enough attention to warrant an inclusion in Wikipedia. For the nonce, therefore, it shall remain a Wikiwannabe only. This link takes you to a copy of the page I constructed for Wikipedia. Yes, it is self-serving, but lest it die alone and unwanted, herewith, The Dixon Algebra.
Added 2015.10.13: a summary of all the things that cascade as consequences from the spinor space T.

Mostly Physics


  • Color and Hypercharge from Mathematics
  • Algebraic Spinor Reduction Yields the Standard Symmetry and Family Structure
    PDF
  • U(1)xSU(2)xSU(3): Original Derivation

Mostly Mathematics


  • Division Algebra Introduction
    PDF
  • 480 Multiplication Tables
  • Two Invariant Multiplication Tables
  • More of this
  • X-Product
    Javascript
  • X-Product E8 Lattices
    Javascript
  • A First XY-Product
  • XY-Product and 16-Dimensional Laminated Lattice
    Javascript
  • 6th Roots of Unity and G2
    Javascript
  • X-Product Modified G2
    Javascript
  • Unravelling Triality with XY-Product
  • More on this
  • Partial Motivation: Aiming at Leech
  • SO(8), Triality, F4, Exceptional Jordan Algebra
  • E6, E7, E8, ?
  • Modified Matrix Product Yields Octonions
  • Some numerology relating to the number 24