The Geometry of the Octonions

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9789814401814: The Geometry of the Octonions
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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, and in fact, all 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.

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"This is an attractive book, with many thought provoking and novel ideas. It is also very well presented with good quality paper and typography, which make it very pleasant to handle." -- David B Fairlie, Emeritus Professor

"This interesting book is recommended to advanced physics and mathematics students and to scientists working in differential geometry. It has a great methodological value because of the multitude of unusual advanced concepts and applications." -- Journal of Geometry and Symmetry in Physics

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Book Description World Scientific Publishing Co Pte Ltd, Singapore, 2015. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # AAC9789814401814

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Book Description World Scientific Publishing Co Pte Ltd, Singapore, 2015. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # AAC9789814401814

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