Octonions and other Division Algebras

Index

Math/Science

Octonion/Physics

Genome/Math

Math/Biology

Games/etc

Products

Algebras, Groups and Physics

Division Algebra Introduction (pdf)

A Totally Cool Mathematical Result

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

U(1)xSU(2)xSU(3): Original Derivation

Octonion Multiplication Tables and Lattices

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

NEWS (17 May 2005): My book ("Division Algebras: ...")
is now published by Springer (which recently bought Kluwer). This link works as of 2005.05.17.

Some articles - open source mathematics and physics:

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.

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

2007 pdf: A short look at the split octonions and associated Lie algebras.

2007 pdf: Why is T complex?

2006 pdf: Advocacy of thinking differently: flame on!

2005 pdf: Mathematics and the Multiverse - Musings. Modified: 2005.08.16.

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) - Modified 2005.10.13.

2003 pdf: Leptoquark Interfamily Mixing from Division Algebras

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.

1995 pdf: Lattice Fibrations - Old paper, but one of my favorite pretty ideas.

HTML version of John Baez's - Octonion review article

Chris Barton's - Magic Squares of Lie Algebras

Some related sites.

Friend Tony, from quarks to Zen.
John Baez, Have Math, Will Surf.
Clifford Algebras and more.
Big buncha info: Division Rings.
Shahn Majid's Quantum Gravity pages.
A History of HyperComplex Numbers.
Apologies to all I've missed. Let me know if you'd like to be included.

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