The Geometry of the Octonions


There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions, and in fact, all symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.

The Geometry of the Octonions
Tevian Dray and Corinne A. Manogue
World Scientific ©2015
ISBN: 978-981-4401-81-4
(publisher website, Amazon)


A prepublication version of the book in wiki format is available here.

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