The Geometry of the Octonions - Hardcover

The book presents a nice addition to the literature and may serve as a primer for more advanced texts. --Zentralblatt MATH

The book under review is a nice addition and will serve as an introduction to more advanced material. --Mathematical Reviews

The book offers an abundance of explicit constructions that are valuable for both beginners and experts, who often tend to underestimate such an approach in the pursuit of abstract ideas ... It is an interesting compilation of an approachable introductory level review on division algebras and their connection to Lie groups. --Journal of Geometry and Symmetry in Physics

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.