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Description - On Quaternions and Octonions by Professor John H. Conway

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 - the octonion projective plane

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Book Details

ISBN: 9781568811345
ISBN-10: 1568811349
Format: Hardback
(234mm x 156mm x mm)
Pages: 172
Imprint: A K Peters
Publisher: Taylor & Francis Inc
Publish Date: 1-Jul-2001
Country of Publication: United States

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