Skip to main content
Log in

The infinite groups of Lie and Cartan Part I, (The transitive groups)

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. E. Cartan, Sur la structure des groupes infinis de transformations,Ann. Ec. Normale, t. 21 (1904) pp. 153–206 and t. 22 (1905) pp. 219–308 or OEuvres, partie II, vol. 2, pp. 571–714.

    MathSciNet  Google Scholar 

  2. E. Cartan, Les sous-groupes des groupes continus de transformations,Ann. Ec. Normale, t. 25 (1908) pp. 57–194 or OEuvres, Partie II, vol. 2, pp. 719–856.

    MathSciNet  Google Scholar 

  3. E. Cartan, Les groupes de transformations continus, infinis, simples,Ann. Ec. Normale, t. 26 (1909) pp. 93–161.

    MathSciNet  Google Scholar 

  4. E. Cartan, Les problèmes d'équivalence, OEuvres, Partie II, vol. 2, pp. 1311–1334.

  5. E. Cartan, La structure des groupes infinis, OEuvres, Partie II, vol. 2, pp. 1335–1384.

  6. E. B. Dynkin, The maximal subgroups of the classical groups,Trans. Amer. Math. Soc., Ser. 2, vol. 6 (1957) pp. 245–378.

    MATH  Google Scholar 

  7. V. Guillemin and S. Sternberg, An algebraic model of transitive differential geometry,Bull. Amer, Math. Soc., vol. 70 (1964) pp. 16–47.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Kobayashi, Le groupe des transformations qui laissent invariant le parallelismeColloque de Topologie de Strasbourg (1954).

  9. B. Kostant, A characterization of the classical groups,Duke Math. J. vol. 25 (1958) pp. 107–123.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Kuranishi, On E. Cartan's prolongation theorem of exterior differential systems,Amer. J. Math., vol. 79 (1957) pp. 1–47.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Kuranishi, On the local theory of continuous infinite pseudo-groups, I, II,Nagoya Math. Journal, vol. 15 (1959) pp. 225–260 and vol. 19 (1961) pp. 55–91.

    MathSciNet  Google Scholar 

  12. Y. Matsushima, Sur les algebras de Lie lineaires semi-involutives,Colloque de topologie de Strasbourg (1954).

  13. A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds,Ann. of Math. vol. 65 (1957) pp. 391–104.

    Article  MathSciNet  Google Scholar 

  14. D. Quillen, Thesis, Ph. D., Harvard University, 1964.

  15. D. C. Spencer, Deformation of structures on manifolds defined by transitive continuous pseudogroups,Ann. of Math. (2) 76, (1962), 306–445.

    Article  MathSciNet  Google Scholar 

  16. S. Sternberg,Lectures on the infinite Lie groups, Harvard, (1961), (multilithed)— (no longer available).

  17. S. Sternberg, “Lectures on Differential Geometry”, New Jersey, Prentice-Hall, Inc., 1964.

    MATH  Google Scholar 

  18. H. Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen.Math. Zeit. 23 (1925) p-271–309, 24 (1926) pp. 329–395.

    Article  MathSciNet  Google Scholar 

  19. O. Zariski and P. Samuel, “Commutative Algebra”, Van Nostrand, Princeton, N. J., 1958.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was partially supported by NSF grant GP-283.

This research was partially supported by NSF grant GP-1217 and by a grant from the Sloan Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Singer, I.M., Sternberg, S. The infinite groups of Lie and Cartan Part I, (The transitive groups). J. Anal. Math. 15, 1–114 (1965). https://doi.org/10.1007/BF02787690

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02787690

Keywords

Navigation