02885nam 22006494a 450 991096989680332120200520144314.097810006877741000687775978042918586104291858639781439864180143986418710.1201/9781439864180 (CKB)1000000000521948(SSID)ssj0000282461(PQKBManifestationID)11207515(PQKBTitleCode)TC0000282461(PQKBWorkID)10317198(PQKB)10886853(MiAaPQ)EBC3059500(Au-PeEL)EBL3059500(CaPaEBR)ebr10159706(OCoLC)922955594(OCoLC)1289860605(FINmELB)ELB143596(EXLCZ)99100000000052194820020926d2003 uy 0engurcn|||||||||txtccrOn quaternions and octonions their geometry, arithmetic, and symmetry /John H. Conway, Derek A. SmithFirst edition.Natick, Mass. AK Petersc2003xii, 159 p. illBibliographic Level Mode of Issuance: Monograph9781568811345 1568811349 Includes bibliographical references (p. 149-152) and index.chapter I I The Complex Numbers -- chapter II II The Quaternions -- chapter III III The Octonions."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.QuaternionsCayley numbers (Algebra)Quaternions.Cayley numbers (Algebra)512/.5Conway John Horton50219Smith Derek Alan1970-737553MiAaPQMiAaPQMiAaPQBOOK9910969896803321On quaternions and octonions1460190UNINA