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Clifford Algebras and the Classical Groups

$79.99 (C)

Part of Cambridge Studies in Advanced Mathematics

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

$ 79.99 (C)

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About the Authors
  • 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

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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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