Geometry Of The Octonions, The by Tevian Dray (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Extremely well done, walks us through the difficulties by adhering to a repeating format.

⭐This is a very well structured and highly readable account of the geometry that links Octonions, Quaternions and Lie groups together and even hints at the promise of developing a Theory of Everything (ToE) in those terms. All calculations are made explicitly and thoroughly and many “mysterious” and exotic properties of Quaternions and Octonions become evident in this way. Highly recommendable reading!!

⭐

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