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On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway [and] Derek A. Smith.

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This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Authors: Conway, John H. (John Horton), Smith, Derek Alan, 1970- (Author)
Other title:Their geometry, arithmetic, and symmetry
Format: eBook
Language:English
Published: Natick, Mass. : CRC Press, [2003]
Subjects:
Quaternions.
Cayley numbers (Algebra)
Quaternions
Algebra
Table of Contents:
  • I. The complex numbers ; Introduction
  • Complex numbers and 2-dimensional geometry
  • II. The quaternions ; Quaternions and 3-dimensional groups
  • Quaternions and 4-dimensional groups
  • The Hurwitz integral quaternions
  • III. 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 octonian projective plane [doublestruck capital]O[italic capital]P².

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