Clifford Algebras and the Classical Groups

A treatment of the theory of Clifford algebras that will be welcomed for its clarity and detail.

Klappentext
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G(subscript 2), and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

Zusammenfassung
Here, Ian Porteous has reworked his previous book on this subject, Topological Geometry, and has expanded and added material to bring the theory of Clifford algebras to the fore. This treatment of the theory of Clifford algebras will be welcomed for its clarity and detail.

Inhalt
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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