2001/12/21 by John C. Baez · 15 citations
Mathematics · #Algebraic and Geometric Analysis #Advanced Topics in Algebra #Geometric and Algebraic Topology
paper · pdf · doi:10.1090/s0273-0979-01-00934-x
openalex publication_date 2001/12/21 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/12
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.