Composition algebras and their automorphisms

  • N. Jacobson


Galois Group Quaternion Algebra Invariant Subgroup Fixed Element Composition 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]
    A. A. Albert,Quadratic froms permitting composition, Ann. of Math., vol. 43 (1942) pp. 161–177.CrossRefMathSciNetGoogle Scholar
  2. [2]
    A. A. Albert and N. Jacobson,On reduced exceptional simple Jordan algebras, Ann. of Math., vol. 66 (1957), pp. 400–417.CrossRefMathSciNetGoogle Scholar
  3. [3]
    E. Artin,Geometric Algebra, New York, 1957.Google Scholar
  4. [4]
    N. Bourbaki,Éléments de Matématique, Livre II, Algèbre, Paris, 1950.zbMATHGoogle Scholar
  5. [5]
    C. Chevalley,Theory of Lie Groups, Princeton, 1946.Google Scholar
  6. [6]
    C. Chevalley,Théorie des Groupes de Lie, Paris, 1951.Google Scholar
  7. [7]
    C. Chevalley,The Algebraic Theory of Spinors, New York, 1954.Google Scholar
  8. [8]
    C. Chevalley,Sur certains groupes simples, Tohoku Math. J., second series, vol. 7 (1955), pp. 14–66.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    L. E. Dickson,Theory of linear groups in an arbitrary field, Trans. Amer. Math. Soc., vol. 2 (1901), pp. 363–394.CrossRefMathSciNetGoogle Scholar
  10. [10]
    J. Dieudonné,Sur les Groupes Classiques, Paris, 1948.Google Scholar
  11. [11]
    J. Dieudonné,La Géométrie des Groupes Classiques, Ergebn. series, Berlin, 1955.Google Scholar
  12. [12]
    H. Freudenthal,Oktaven, Ausnahmegruppen und Oktavengeometrie, Utrecht, 1951.Google Scholar
  13. [13]
    A. Hurvitz,Über die Composition der quadratischen Formen von beliebig vielen Variablen, Gott. Nachrichten, 1898, pp. 309–316.Google Scholar
  14. [14]
    N. Jacobson,Cayley numbers and normal simple Lie algebras of type G, Duke Math. Jour., vol. 5 (1939), pp. 775–783.zbMATHCrossRefGoogle Scholar
  15. [15]
    N. Jacobson,Abstract derivation and Lie algebras, Trans. Amer. Math. Soc., vol. 42 (1937), pp. 206–224.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    I. Kaplansky,Infinite dimensional quadratic forms permitting composition, Proc. Amer. Math. Soc., vol. 4 (1953), pp. 956–960.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    F. Kasch,Über den Automorphismenring einfacher Algebren, Arch. Math., vol. 6 (1954), pp. 59–64.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    F. Levi and v. d. Waerden,Über eine bisondere Klasse von Gruppen, Hamb. Abhandl., vol. 9 (1933), pp. 154–158.Google Scholar
  19. [19]
    Y. V. Linnik,Quaternions and Cayley numbers; some applications of the arithmetic of quaternions, Uspehi Matem. Nauk. vol. 4 no. 5 (1949), pp. 49–98 (Russian).zbMATHMathSciNetGoogle Scholar
  20. [20]
    M. Zorn,Alternativkorpern und quadratische Systeme, Hamb. Abhandl., vol. 9 (1953), pp. 393–402.Google Scholar
  21. [21]
    M. Zorn,The automorphisms of Cayley's non-associative algebra, Proc. Nat. Acad. Sci., vol. 21 (1935), pp. 355–358.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer 1958

Authors and Affiliations

  • N. Jacobson
    • 1
  1. 1.Paris

Personalised recommendations