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.

### 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.

### Reviews

Review of the hardback: 'This book covers material which you would hardly find in such a compact form elsewhere. It is very pleasant to have all these things together and so nicely arranged.' European Mathematical Society Journal

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