On Quaternions and Octonions
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On Quaternions and Octonions by Professor John H. Conway
Book DescriptionThis 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. 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 authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.
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Book DetailsISBN: 9781568811345
(234mm x 156mm x 15mm)
Imprint: A K Peters
Publisher: Taylor & Francis Inc
Publish Date: 1-Jul-2001
Country of Publication: United States
Books By Author Professor John H. Conway
Book of Numbers, Hardback (February 1998)» View all books by Professor John H. Conway
Gives a look at numbers and their roles from language to flowers to the imagination. This title includes numerical topics and concepts.
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