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    On Quaternions and Octonions (Hardback) By (author) John H. Conway, By (author) Derek A. Smith

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    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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  • Full bibliographic data for On Quaternions and Octonions

    Title
    On Quaternions and Octonions
    Authors and contributors
    By (author) John H. Conway, By (author) Derek A. Smith
    Physical properties
    Format: Hardback
    Number of pages: 160
    Width: 157 mm
    Height: 230 mm
    Thickness: 15 mm
    Weight: 408 g
    Language
    English
    ISBN
    ISBN 13: 9781568811345
    ISBN 10: 1568811349
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 01
    B&T General Subject: 710
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    Libri: I-MA
    B&T Merchandise Category: STX
    DC22: 512.5
    BIC subject category V2: PBF
    Warengruppen-Systematik des deutschen Buchhandels: 16240
    BISAC V2.8: MAT012000
    DC22: 512/.5
    BISAC V2.8: MAT034000, MAT002050
    BIC subject category V2: PBMW
    DC21: 516.35
    LC subject heading: ,
    LC classification: QA196 .C66 2003
    Thema V1.0: PBF, PBMW
    Publisher
    Taylor & Francis Inc
    Imprint name
    A K Peters
    Publication date
    23 January 2003
    Publication City/Country
    Natick
    Review quote
    "Conway and Smith's book is a wonderful introduction to the normed division algebras ... They develop these number systems from scratch, explore their connections to geometry, and even study number theory in quaternionic and octonionic versions of the integers. ... a lucid and elegant introduction. ... remarkably self-contained. It assumes no knowledge of number theory, string theory, Lie theory, or lower-case Gothic letters." -John C. Baez, Bulletin of the American Mathematical Society, January 2005 "A resonant spike above background noise in one parameter as another parameter is varied is a frequent indicator..." -Geoffrey Dixon, Mathematical Intelligencer, May 2004 "Those readers who are fascinated by the links between geometry and groups will find that this book gives them new insights." -Hugh Williams, The Mathematical Gazette, July 2004 "This is a beautiful and fascinating book on the geometry and arithmetic of the quaternion algebra and the octonion algebra. ... most intriguing to read: it is an excellent exposition of very attractive topics, and it contains several new and significant results." -Theo Grundhofer, Mathematical Reviews, 2003