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Clifford Algebras and the Classical Groups


Part of Cambridge Studies in Advanced Mathematics

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

£ 61.99

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About the Authors
  • 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.

    Reviews & endorsements

    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

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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.

  • Author

    Ian R. Porteous, University of Liverpool

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