On quaternions and octonions : their geometry, arithmetic, and symmetry /
"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 symm...
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| Format: | eBook |
| Language: | English |
| Language Notes: | English. |
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Natick, Mass. :
AK Peters,
©2003.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | "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. 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."--Provided by publisher. |
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| Physical Description: | 1 online resource (xii, 159 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 149-152) and index. |
| ISBN: | 9781439864180 1439864187 1568811349 9781568811345 0429185863 9780429185861 1000687775 9781000687774 |