Clifford Algebras and the Classical Groups
Clifford Algebras and the Classical Groups
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
Product details
October 1995Hardback
9780521551779
308 pages
236 × 157 × 23 mm
0.555kg
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.
