Octonions and other Division Algebras

Index

Math/Science

Octonion/Physics

Genome/Math

Math/Biology

Games/etc

Products

NEWS (18 November 2011):
"Division Algebras, Lattices, Physics, Windmill Tilting",
a manuscript of 17 years of research since the publication of the first book,
now available on Amazon (USA sales).

A possible international sales link. However, there are now a number
of countries whose Amazon sites (or Borders) claim to be able to sell the book.
If you have tried and failed to purchase, please email me at:
gdixon@7stones.com

Half of this volume is devoted to relationships of the division algebras to lattice theory;
half of the material extends and illuminates the material in book 1 concerning the algebra T,
and the role it is maintained it plays in the "Algebraic Design of Physics";
and the remaining third ; ) of this new volume is lattice related numerology,
as well as some history, and opinion.
NEWS (17 May 2005): "Division Algebras: Octonions, Quaternions, Complex Numbers,
and the Algebraic Design of Physics"
is now published by Springer (which recently bought Kluwer). This link works as of 2005.05.17.

pdf of "Algebraic Spinor Reduction Yields the Standard Symmetry and Family Structure"

Some numerology relating to the number 24
(Too much free time, but not enough for anything deep.)

Some articles - open source mathematics and physics:

2013 pdf: Seeable Matter; Unseeable Antimatter
A version of this idea that was presented at a conference in 2013.

2012 pdf: Matter Universe: Message in the Mathematics
T explains why our universe is composed of matter at the expense of anti-matter. Modified: 2012.09.24
(First ever paper rejected by hep-th. Well well. I must endeavor to be less flippant in future.
But this is a really nice idea - and since I believe it's right, it's the most important paper I've
had on here in 20 years.)

2012 pdf: Division algebras, Clifford algebras, and periodicity.
Thoughts on periodicities of order 2, 4, 8 and 24. Modified: 2012.04.02

2010 pdf: Division algebras as spinors; idempotents; symmetries; particles; interactions.
Lengthy version of T maths, spinors, idempotents, and physics, arising from discussions at a recent
conference in Denver. Best yet, in many ways. Modified: 2009.07.28

2009 pdf: A triple product generalization for the complex algebra C,
and I hope a firmer step to accomplishing what I set out to investigate
in the incomplete paper below. Modified: 2010.02.07

2008 pdf: A rapidly evolving search for a triple product for 24-space,
and I believe the most important idea presented here in 3 years. Modified: 2010.05.21

2007 pdf: Order 8 and order 24 lattice periodicity. - not deep, probably not original,
but ...

2004 pdf: Division Algebras: Family Replication - Appeared in J. of Math. Physics, October 2004.
C ⊗ H² ⊗ O³ accounts for the Standard model, leptoquark family structure, AND family replication. Modified: 2004.04.18.

2005 pdf: Integral Octonions and the Octonion XY-Product and more (a work in progress) - Last modified 2009.12.02.

2003 pdf: Parity Nonconservation from Division Algebras
Continuing development of multifamily model based on C x H² x O³, we find an algebraic origin for parity nonconservation.

2002 pdf: Division Algebras: Family Replication - Earlier version of the C ⊗ H² ⊗ O³ replaced above.

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

2000 pdf: Tensored Division Algebras: Resolutions of the Identity and Particle Physics

'A Fire in the Night' has been removed to avoid its being any longer misinterpreted.

Some related sites.