Hurwitz Problem

  • Takashi Ono
Part of the The University Series in Mathematics book series (USMA)


We have a homework problem to prove Theorem 5. The theorem provides us with an algebraic criterion for the existence of a Hopf map of the first kind. Although the ground field in this context is the real numbers, we start with an arbitrary field K of characteristic ≠2.


Orthogonal Basis Left Ideal Division Algebra Clifford Algebra Simple Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Chevalley, Algebraic Theory of Spinors, Columbia Univ. Press, New York (1954).MATHGoogle Scholar
  2. 2.
    P. Hilton, General Cohomology Theory and K-Theory, London Math. Soc. Lect. Note Ser., 1, Cambridge Univ. Press (1971).Google Scholar
  3. 3.
    A. Hurwitz, Mathematische Werke, Bd. 2., Birkhäuser (1964).Google Scholar
  4. 4.
    D. Husemoller, Fibre Bundles, Grad. Texts in Math., 20, Springer, New York-Heidelberg-Berlin (1975).MATHGoogle Scholar
  5. 5.
    T. Y. Lam, Algebraic Theory of Quadratic Forms, W. A. Benjamin, Reading, MA (1973).MATHGoogle Scholar
  6. 6.
    I. Satake, Stories of Lie Algebras, Nipponhyoron, Tokyo (1987).Google Scholar
  7. 7.
    R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York (1966).MATHGoogle Scholar
  8. 8.
    N. Steenrod, Topology of Fibre Bundles, Princeton Univ. Press, Princeton, NJ, (1951).MATHGoogle Scholar
  9. 9.
    J. A. Tyrrell and J. G. Semple, Generalized Clifford Parallelism, Cambridge Tracts in Math., 61, Cambridge Univ. Press, Cambridge, UK (1971).MATHGoogle Scholar

Copyright information

© Takashi Ono 1994

Authors and Affiliations

  • Takashi Ono
    • 1
  1. 1.The Johns Hopkins UniversityBaltimoreUSA

Personalised recommendations