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Clifford Algebras and the Classical Groups
     

Clifford Algebras and the Classical Groups

by Ian R. Porteous
 

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ISBN-10: 0521551773

ISBN-13: 9780521551779

Pub. Date: 12/28/2004

Publisher: Cambridge University Press

This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author includes an exhaustive treatment of all the generalizations of the classical groups, as well as an excellent

Overview

This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author includes an exhaustive treatment of all the generalizations of the classical groups, as well as an excellent exposition of the classification of the conjugation anti-involution of the Clifford algebras and their complexifications. Toward the end of the book, the author introduces ideas from the theory of Lie groups and Lie algebras. This treatment of Clifford algebras will be welcomed by graduate students and researchers in algebra.

Product Details

ISBN-13:
9780521551779
Publisher:
Cambridge University Press
Publication date:
12/28/2004
Series:
Cambridge Studies in Advanced Mathematics Series , #50
Pages:
308
Product dimensions:
5.98(w) x 8.98(h) x 0.83(d)

Table of Contents

1. Linear spaces; 2. Real and complex algebras; 3. Exact sequences; 4. Real quadratic spaces; 5. The classification of quadratic spaces; 6. Anti-involutions of R(n); 7. Anti-involutions of C(n); 8. Quarternions; 9. Quarternionic linear spaces; 10. Anti-involutions of H(n); 11. Tensor products of algebras; 12. Anti-involutions of 2K(n); 13. The classical groups; 14. Quadric Grassmannians; 15. Clifford algebras; 16. Spin groups; 17. Conjugation; 18. 2x2 Clifford matrices; 19. The Cayley algebra; 20. Topological spaces; 21. Manifolds; 22. Lie groups; 23. Conformal groups; 24. Triality.

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