A01=Corinne A Manogue
A01=Tevian Dray
Author_Corinne A Manogue
Author_Tevian Dray
Category=PBF
Category=PBM
Division Algebras
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Non-Associative Algebras
Octonions
Particle Physics
Quaternions
Theory of Everything
Product details
- ISBN 9789811218187
- Publication Date: 29 May 2015
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Paperback
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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. In fact, all (continuous) 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.
