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Look Inside Clifford Algebras and the Classical Groups

Clifford Algebras and the Classical Groups

$79.99 (C)

Part of Cambridge Studies in Advanced Mathematics

Author: Ian R. Porteous, University of Liverpool

Date Published: August 2009
availability: Available
format: Paperback
isbn: 9780521118026

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About the Authors

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.
Reviews & endorsements
"Porteous' new book is welcome for its coverage and detail and the reliability of its text. Porteous' presentation of the subject matter sets a standard by which others may be judged." Peter R. Law, Mathematical Reviews

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Product details
- Date Published: August 2009
- format: Paperback
- isbn: 9780521118026
- length: 308 pages
- dimensions: 229 x 152 x 18 mm
- weight: 0.46kg
- availability: Available
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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Author
Ian R. Porteous, University of Liverpool