COLLECTED BY
Organization:
Alexa Crawls
Starting in 1996,
Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the
Wayback Machine after an embargo period.
this data is currently not publicly accessible.
The Wayback Machine - https://web.archive.org/web/20090421054044/http://math.ucr.edu:80/home/baez/octonions/octonions.html
Next: Introduction
Abstract:
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.
Table of Contents:
- Introduction
- Preliminaries
- Constructing the Octonions
- The Fano Plane
- The Cayley-Dickson Construction
- Clifford Algebras
- Spinors and Trialities
- Octonionic Projective Geometry
- Projective Lines
- OP1 and Bott Periodicity
- OP1 and Lorentzian Geometry
- OP2 and the Exceptional Jordan Algebra
- Exceptional Lie Algebras
- G2
- F4
- The Magic Square
- E6
- E7
- E8
- Conclusions
- Acknowledgements
- Bibliography
This website also contains some extra stuff, namely:
And if all this is too hard for you, try this two-part feature in Plus Magazine:
and
in which Helen Joyce and I have a fun nontechnical chat about the real numbers, complex numbers, quaternions and octonions.
© 2004 John Baez
baez@math.removethis.ucr.andthis.edu