Notice bibliographique
- Notice
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Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Dray, Tevian
Manogue, Corinne A.
Titre(s) : The geometry of the octonions [Texte imprimé] / Tevian Dray,... Corinne A. Manogue,...
Publication : Hackensack, New Jersey : World scientific, copyright 2015
Description matérielle : 1 vol. (XVII-210 p.) : ill. ; 24 cm
Note(s) : Bibliogr. p. 199-203. Index
There are precisely two further generalizations of the real and complex numbers, namely,
the quaternions and the octonions. The quaternions naturally describe rotations in
three dimensions. In fact, all (continuous) symmetry groups are based on one of these
four number systems. This book provides an elementary introduction to the properties
of the octonions, with emphasis on their geometric structure. Elementary applications
covered include the rotation groups and their spacetime generalization, the Lorentz
group, as well as the eigenvalue problem for Hermitian matrices. In addition, more
sophisticated applications include the exceptional Lie groups, octonionic projective
spaces, and applications to particle physics including the remarkable fact that classical
supersymmetry only exists in particular spacetime dimensions.--Publisher website
Sujet(s) : Octonions
Indice(s) Dewey : 512.5 (23e éd.) = Algèbre linéaire
Identifiants, prix et caractéristiques : ISBN 9789814401814. - ISBN 9814401811 (rel.)
Identifiant de la notice : ark:/12148/cb45792096k
Notice n° :
FRBNF45792096
(notice reprise d'un réservoir extérieur)
Table des matières : I. Number Systems ; The Geometry of the Complex Numbers ; The Geometry of the Quaternions ; The Geometry of the Octonions ; Other Number Systems ; II. Symmetry Groups ; Some Orthogonal Groups ; Some Unitary Groups ; Some Symplectic Groups ; Symmetry Groups over Other Division Algebras ; Lie Groups and Lie Algebras ; The Exceptional Groups ; III. Applications ; ; Division Algebras in Mathematics ; Octonionic Eigenvalue Problems ; The Physics of the Octonions ; Magic Squares.