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The octonions


Author: John C. Baez
Journal: Bull. Amer. Math. Soc. 39 (2002), 145-205
MSC (2000): Primary 17-02, 17A35, 17C40, 17C90, 22E70
Published electronically: December 21, 2001
Erratum: Bull. Amer. Math. Soc. (N.S.) 42 (2005), 213
MathSciNet review: 1886087
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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.


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Additional Information

John C. Baez
Affiliation: Department of Mathematics, University of California, Riverside, CA 92521
Email: baez@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-01-00934-X
Received by editor(s): May 31, 2001
Received by editor(s) in revised form: August 2, 2001
Published electronically: December 21, 2001
Article copyright: © Copyright 2001 John C. Baez