© 2008

Quadratic Mappings and Clifford Algebras


  • The study of Clifford algebras leads to sophisticated theories involving noncommutative algebras over a ring, e.g., Azumaya algebras, Morita theory, separability

  • Provides a self-contained introduction to commutative algebra

  • Prerequisites are only elementary algebra and linear and multilinear algebra over fields (and a bit over rings)


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pages 53-103
  3. Pages 105-174
  4. Pages 391-438
  5. Back Matter
    Pages 489-504

About this book


After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve more original methods: interior multiplications allow an effective treatment of deformations of Clifford algebras; the relations between automorphisms of quadratic forms and Clifford algebras are based on the concept of the Lipschitz monoid, from which several groups are derived; and the Cartan-Chevalley theory of hyperbolic spaces becomes much more general, precise and effective.


Clifford algebra Lipschitz group algebra hyperbolic space orthogonal group quadratic form quadratic mapping

Authors and affiliations

  1. 1.Institut Fourier (Mathématiques)Université Grenoble ISaint-Martin d’Hères CedexFrance
  2. 2.Département des Sciences mathématiquesUniversité Montpellier IIMontpellier Cedex 5France

Bibliographic information

  • Book Title Quadratic Mappings and Clifford Algebras
  • Authors Jacques Helmstetter
    Artibano Micali
  • DOI
  • Copyright Information Birkhäuser Verlag AG 2008
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-7643-8605-4
  • eBook ISBN 978-3-7643-8606-1
  • Edition Number 1
  • Number of Pages XIII, 504
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site