On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry

John Horton Conway; Derek Smith

ISBN 10: 1568811349 / ISBN 13: 9781568811345

Verlag: A K Peters/CRC Press, 2003

Beschreibung

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Bestandsnummer des Verkäufers Q-1568811349

Bibliografische Details

• Titel: On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry
• Verlag: A K Peters/CRC Press
• Erscheinungsjahr: 2003
• Sprache: Englisch
• ISBN-10: 1568811349
• ISBN-13: 9781568811345
• Einband: hardcover
• Zustand: New
• Gewicht: 16 Unzen

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

John H. Conway, Derek A. Smith