References
É. Cartan, Über die einfachen Transformationsgruppen,Leipzig Ber., 1893, pp. 395–420; reprint,Oeuvres complètes, Vol. I, no. 1, Paris: Gauthier-Villars (1952), 107–132. 1b.-, Sur la structure des groupes de transformations finis et continus, Thèse, Paris Nony, 1894; reprint,Oeuvres complètes, vol. I, no. 1, Paris: Gauthier Villars (1952), 137–287.
—, Les groupes projectifs qui ne laissent invariants aucune multiplicité plane,Bull. Soc. Sci. Math. 41 (1913), 53–96.
—, Les groupes réels simples finis et continus,Ann. Sci. École Norm. Sup. 31 (1914), 263–355.
—, Groupes simples clos et ouverts et géométrie riemannienne,J. Math. Pures Appl. (9) 8 (1929), 1–33.
C. Chevalley, Sur la classification des algebrès de Lie simples et de leurs représentations,C.R. Acad. Sci. Paris 227 (1948), 1136–1138.
—, Sur certains groupes simples,Tôhoku Math. J. 7 (1955), 14–66.
A. J. Coleman, The greatest mathematical paper of all time,The Mathematical Intelligencer 11, no. 3 (1989), 29–38.
F. Engel, Sur un groupe simple à quatorze paramètres,C.R. Acad. Sci. Paris 116 (1893), 786–788.
—, Wilhelm Killing (obituary),Jber. Deutsch. Math. Verein. 39 (1930), 140–154.
Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie algebra,Trans. Amer. Math. Soc. 70 (1951), 28–96.
T. Hawkins, Wilhelm Killing and the structure of Lie algebras.Archive for Hist. Exact. Sci. 26 (1982), 126–192.
-, Élie Cartan and the prehistory of the representation theory of Lie algebras, preprint 1984.
S. Helgason,Differential Geometry, Lie groups and Symmetric Spaces, New York: Academic Press (1978).
—, Invariant differential equations on homogeneous manifolds,Bull. Amer. Math. Soc. 83 (1977), 751–774.
—, Some results in invariant theory,Bull. Amer. Math. Soc. 68 (1962), 367–371.
W. Killing, Die Zusammensetzung der stetigen endlichen Transformationsgruppen II,Math. Ann. 33 (1889), 1–48.
E. E. Levi, Sulla struttura dei gruppi continui.Atti Accad. Sci. Torino 60 (1905), 551–565.
S. Lie and F. Engel,Theorie der Transformationsgruppen, 3 vols. Leipzig: Teubner (1888–1893).
R. Richardson, Compact real forms of a semisimple Lie algebra.J. Differential Geometry 2 (1968), 411–420.
H. Weyl,The structure and representations of continuous groups, New Jersey: Inst. Adv. Study Princeton, Notes. (1935).
E. Witt, Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe,Abh. Math. Sem. Univ. Hamburg 14 (1941), 289–322.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Helgason, S. A Centennial: Wilhelm Killing and the Exceptional Groups. The Mathematical Intelligencer 12, 54–57 (1990). https://doi.org/10.1007/BF03024019
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03024019