Clifford Algebras and the Classical Groups

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

Ian R. Porteous (Author)

9780521118026, Cambridge University Press

Paperback, published 6 August 2009

308 pages
22.9 x 15.2 x 1.8 cm, 0.46 kg

Review of the hardback: 'Plenty of examples make Porteous's book pleasant to read.' Mathematica

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 G2, 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.

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.

Subject Areas: Algebra [PBF]