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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 symmetries...

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Detalles Bibliográficos
Autores principales: Conway, John, Smith, Derek
Lenguaje:eng
Publicado: CRC Press 2003
Materias:
Acceso en línea:http://cds.cern.ch/record/2114442
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author Conway, John
Smith, Derek
author_facet Conway, John
Smith, Derek
author_sort Conway, John
collection CERN
description 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.
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spelling cern-21144422021-04-21T19:57:16Zhttp://cds.cern.ch/record/2114442engConway, JohnSmith, DerekOn quaternions and octonions: their geometry, arithmetic, and symmetryMathematical Physics and MathematicsThis 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.CRC Pressoai:cds.cern.ch:21144422003
spellingShingle Mathematical Physics and Mathematics
Conway, John
Smith, Derek
On quaternions and octonions: their geometry, arithmetic, and symmetry
title On quaternions and octonions: their geometry, arithmetic, and symmetry
title_full On quaternions and octonions: their geometry, arithmetic, and symmetry
title_fullStr On quaternions and octonions: their geometry, arithmetic, and symmetry
title_full_unstemmed On quaternions and octonions: their geometry, arithmetic, and symmetry
title_short On quaternions and octonions: their geometry, arithmetic, and symmetry
title_sort on quaternions and octonions: their geometry, arithmetic, and symmetry
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2114442
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AT smithderek onquaternionsandoctonionstheirgeometryarithmeticandsymmetry