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arXiv:math/0105155math.RA

The Octonions

John C. Baez

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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.

arXiv comments
56 pages LaTeX, 11 Postscript Figures, some small corrections
Journal reference
Bull.Am.Math.Soc.39:145-205,2002
DOI
Subjects
math.RARings and Algebras hep-thHigh Energy Physics, Theory math.HOHistory and Overview math.QAQuantum Algebra math.RTRepresentation Theory

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  1. Quaternion Algebras 1 comment

    • Baez wrote some ideas in [1], one I'm liking connects Lorentz group in dimensions 3,4,6 and 10 with the modular group SL(2,Z) that is at a crossroads of several hardcore math themes. For Lie algebras: sl(2, R) ≅ so(2,1) sl(2, C) ≅ so(3,1) sl(2, H) ≅ so(5,1) sl(2, O) ≅ so(9,1)…

      jesuslopView on HNParent context

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