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Singer, I. M.; Sternberg, Shlomo

The infinite groups of Lie and Cartan. I: The transitive groups. (English) Zbl 0277.58008

J. Anal. Math. 15, 1-114 (1965).
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Cited in 6 Reviews
Cited in 142 Documents

MSC:

58H05 Pseudogroups and differentiable groupoids
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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\textit{I. M. Singer} and \textit{S. Sternberg}, J. Anal. Math. 15, 1--114 (1965; Zbl 0277.58008)
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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.
[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. · JFM 39.0206.04
[3] E. Cartan, Les groupes de transformations continus, infinis, simples,Ann. Ec. Normale, t. 26 (1909) pp. 93–161. · JFM 40.0193.02
[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. · Zbl 0077.03403
[7] V. Guillemin and S. Sternberg, An algebraic model of transitive differential geometry,Bull. Amer, Math. Soc., vol. 70 (1964) pp. 16–47. · Zbl 0121.38801
[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. · Zbl 0079.04301
[10] M. Kuranishi, On E. Cartan’s prolongation theorem of exterior differential systems,Amer. J. Math., vol. 79 (1957) pp. 1–47. · Zbl 0077.29701
[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. · Zbl 0212.56501
[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. · Zbl 0079.16102
[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. · Zbl 0124.38601
[16] S. Sternberg,Lectures on the infinite Lie groups, Harvard, (1961), (multilithed)– (no longer available). · Zbl 0131.26802
[17] S. Sternberg, ”Lectures on Differential Geometry”, New Jersey, Prentice-Hall, Inc., 1964. · Zbl 0129.13102
[18] H. Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen.Math. Zeit. 23 (1925) p-271–309, 24 (1926) pp. 329–395. · JFM 51.0319.01
[19] O. Zariski and P. Samuel, ”Commutative Algebra”, Van Nostrand, Princeton, N. J., 1958. · Zbl 0081.26501
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