Résumé
This book investigates the geometry of the quaternion and octonion algebras. Following a comprehensive 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 half 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.
Topics covered include: history; the geometry of complex numbers; quaternions and 3-dimensional groups; quaternions and 4-dimensional groups; the Hurwitz integral quaternions; the composition algebras, Moufang loops; octonions and 8-dimensional geometry; integral octonions; and the octonion projective plane.
Sommaire
- The Complex Numbers
- Introduction
- Complex Numbers and 2-Dimensional Geometry
- The Quaternions
- Quaternions and 3-Dimensional Groups
- Quaternions and 4-Dimensional Groups
- The Octonions
- The Composition Algebras
- Moufang Loops
- Octonions and 8-Dimensional Geometry
- The Octavian Integers O
- Automorphisms and Subrings of O
- Reading O mod 2
- The Octonion Projective Plane OP2
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | AK Peters |
| Auteur(s) | John H. Conway, Derek Smith |
| Parution | 04/04/2003 |
| Nb. de pages | 160 |
| Format | 15,5 x 23,5 |
| Couverture | Relié |
| Poids | 360g |
| Intérieur | Noir et Blanc |
| EAN13 | 9781568811345 |
| ISBN13 | 978-1-56881-134-5 |
Avantages Eyrolles.com
Consultez aussi
- Les meilleures ventes en Graphisme & Photo
- Les meilleures ventes en Informatique
- Les meilleures ventes en Construction
- Les meilleures ventes en Entreprise & Droit
- Les meilleures ventes en Sciences
- Les meilleures ventes en Littérature
- Les meilleures ventes en Arts & Loisirs
- Les meilleures ventes en Vie pratique
- Les meilleures ventes en Voyage et Tourisme
- Les meilleures ventes en BD et Jeunesse
