The Octonions
Rings and Algebras
2011-09-28 v4 High Energy Physics - Theory
History and Overview
Quantum Algebra
Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0105155,
title = {The Octonions},
author = {John C. Baez},
journal= {arXiv preprint arXiv:math/0105155},
year = {2011}
}
Comments
56 pages LaTeX, 11 Postscript Figures, some small corrections