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.
By:
Tevian Dray (Oregon State Univ Usa), Corinne A Manogue (Oregon State Univ, Usa) Imprint: World Scientific Publishing Co Pte Ltd Country of Publication: Singapore ISBN:9789814401814 ISBN 10: 9814401811 Pages: 228 Publication Date:10 April 2015 Audience:
College/higher education
,
Further / Higher Education
Format:Hardback Publisher's Status: Unspecified
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.
