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OctoShop III

Most people visiting this page are actually after this other page.

The third Octoshop is over, and thanks to all participants it was a great success. Everyone who wanted to talk did so to their heart's content, and everyone who wanted to interrupt and harass did so till they could do no more. Much was learned, and many doors opened.
Special thanks to Tony Sudbery for saying yes to my suggestion that the next one should be held in York, and especially to Chris Barton without whom the participants would have ended up milling around outside with no place to talk, sleep, or eat.


Suggestion: henceforth this page will link to any material on the division algebras and other exceptional and/or special mathematical structures. Send me suggestions. While I'm at it, re the problem of nested 6th roots of unity:
If x and y are unit octonions, z = xy*, u3 = z, and v3 = x,
then the octonion x,y-product ((Ax)(y*B))
can be written (modulo some G2 transformation) as
G-1[G[A]G[B]] where

G[A] = (v*u2v)(v*Av)(v*uv).

This is a double nesting, so presumably it requires 2 more nestings to do all of SO(8) than to do G2 alone - conjecture at this point.

Note: it was suggested that a 7 deep nesting was required to get all of SO(8). At
it is claimed (probably from a Conway reference) that a 7 deep one sided nesting is required.

Geoffrey Dixon

My technical pages:
Division Algebras,
Lie Algebras,
Lie Groups,
Spinors and Lattices

This page updated:
18 Novemebr 2002

Those attending (Tony Smith attended
in spirit, which he sent to all participants
in the form of a CD)::

  • Tony Sudbery
  • Geoffrey Dixon
  • Tevian Dray
  • Corinne Manogue
  • Pertti Lounesto
  • Tony Smith
  • Chris Barton
  • Shahn Majid
  • J.E.Mebius
  • Ian Porteous
  • Paul Hammond
  • Nicholas Jackson
  • Gisele Ducati
  • Rolf Dahm
  • Mariano Santander

pdf of 1999 paper:
Algebraic Spinor Reduction Yields the Standard Symmetry and Family Structure

pdf of 2000 paper (modified 7 September 2000):
Tensored Division Algebras: Resolutions of the Identity and Particle Physics

pdf of 2002 paper on leptoQuark family replication:
Division Algebras: Family Replication

Some related sites.

Index Octonions Mathematics and Physics Interactive Tutorials Resume