On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry (Hardback)

Condition

LIKE NEW: This book is in excellent, like-new condition.

Product Details

From the back cover: "This book is about the geometry of the quaternion and octonion algebras. Following an historical introduction, the special properties of 3- and 4-dimensional Euclidean spaces are illuminated using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second part of the book discusses the less familiar octonion algebra, concentrating on its remarkable 'triality symmetry' after an appropriate study of Moufang loops. The arithmetics of the quaternions and octonions are also described, and the book concludes with a new theory of octonion factorization."

BRIEF CONTENTS

I. The Complex Numbers

1. Introduction
2. Complex Numbers and 2-Dimensional Geometry

II. The Quaternions

3. Quaternions and 3-Dimensional Groups
4. Quaternions and 4-Dimensional Groups
5. The Hurwitz Integral Quaternions

III. The Octonions

6. The Composition Algebras
7. Moufang Loops
8. Octonions and 8-Dimensional Geometry
9. The Octavian Integers O
10. Automorphisms and Subrings of O
11. Reading O Mod 2
12. The Octonion Projective Plane OP²

The book concludes with Bibliography and Index.