
Geometry Of The Octonions, The
World Scientific Publishing Co Pte Ltd
Published on 29. May 2015
Book
Hardback
228 pages
978-981-4401-81-4 (ISBN)
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.
More details
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 17 mm
Weight
490 gr
ISBN-13
978-981-4401-81-4 (9789814401814)
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Schweitzer Classification
Persons
Content
Introduction; Division Algebras; Rotations; Lorentz Transformations; Spinors; The Right Eigenvalue Problem; The Exceptional Jordan Algebra; The Jordan Eigenvalue Problem; Lie Groups and Lie Algebras; Exceptional Lie Groups; The Dirac Equation; Octonionic Projective Spaces.