Octonion Algebra
A presentation of the algebra and its connection to physics
This website is a repository for papers I have written describing my research into the
application of Octonion Algebra to Physics. Understanding the application requires an
understanding of Octonion Algebra itself. There are perspectives on the algebra that
anyone interested in Octonions for any reason may find enlightening, and will not be able
to find anywhere else for now.

Highlights of original work

There are only two truly different multiplication tables for Octonion Algebra, not 480.
They can be classified as Left Octonion or Right Octonion. For a given set of 7
permutation triplets, there are only 8 Right and 8 Left Octonion Algebras, not 128.

Creation methods for all possible valid Octonion Algebras and mappings between them.

The Law of Octonion Algebraic Invariance, and the Octonion Variance Sieve Process.

The Octonion Ensemble Derivative Form as the foundation for Octonion Calculus.

The Invariant 8-current and the Invariant Action Function (work-force Octonion form).

Applying the Law of Algebraic Invariance to convert the Action Function to an equivalent
integrable form. Equating the Action Function to its integrated form to produce the
Octonion Conservation of Energy and Momentum Equations. Electrodynamics is fully
covered as a subset of the presentation.
Copyright 2008-2010 Richard Lockyer
email: rick@octospace.com
More PDF Files Here
Hadamard Matrix Connection to the Octonions
Quaternion Doubling for all Octonion Algebras
Octonion Torque Variances
16 Octonion Algebras - 480 Representations
Somewhat new
Somewhat new
Somewhat New