Conjugate classes of Cartan subalgebras in real semisimple Lie algebras

Mitsuo SUGIURA

doi:10.2969/jmsj/01140374

Mitsuo SUGIURA

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JOURNAL FREE ACCESS

1959 Volume 11 Issue 4 Pages 374-434

DOI https://doi.org/10.2969/jmsj/01140374

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Published: 1959 Received: July 04, 1959 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Cartan, Les groupes réels simple finis et continus, Ann. Éc. Norm., 31 (1914), 263-355.
2) E. Cartan, Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Éc. Norm., 44 (1927), 345-467.
3) E. Cartan, Groupes simples clos et ouverts et géométrie riemannienne, J. Math. pures et appliquées, 8 (1929), 133.
4) C. Chevalley, (a) Theory of Lie groups, I. Princeton, 1946. (b) Théorie des groupes de Lie, t. III, Hermann, Paris, 1955.
5) F. Gantmacher, On the classification of real simple Lie groups, Mat. Sbornik, 5 (1939), 217-250.
6) Harish-Chandra, The characters of semisimple Lie groups, Trans. Amer. Math. Soc., 83 (1956), 98-163.
7) G. A. Hunt, A theorem of E. Cartan, Proc. Amer. Math. Soc., 7 (1956), 307-308.
8) N. Iwahori and I. Satake, On Cartan subalgebras of a Lie algebra, Kodai Math. Sem. Rep., 3 (1950), 57-60.
9) B. Kostant, Conjugacy of real Cartan subalgebras, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 967-970.
10) G. D. Mostow, A new proof of E. Cartan's theorem on the topology of semisimple groups, Bull. Amer. Math. Soc., 55 (1949), 969-980.
11) S. Murakami, Supplements and corrections to my paper: On the automorphisms of a real semisimple Lie algebra, J. Math. Soc. Japan, 5 (1953), 105-112.
12) L. S. Pontrjagin, Continuous groups (in Russian), second edition, Moscow, 1954.
13) H. Weyl, The structure and representations of continuous groups. The Institute for Advanced Study, Princeton, 1935.

Right : [1] E. Cartan, Les groupes réels simple finis et continus, Ann. Éc. Norm., 31 (1914), 263-355.
[2] E. Cartan, Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Éc. Norm., 44 (1927), 345-467.
[3] E. Cartan, Groupes simples clos et ouverts et géométrie riemannienne, J. Math. pures et appliquées, 8 (1929), 133.
[4] C. Chevalley, (a) Theory of Lie groups, I. Princeton, 1946. (b) Théorie des groupes de Lie, t. III, Hermann, Paris, 1955.
[5] F. Gantmacher, On the classification of real simple Lie groups, Mat. Sbornik, 5 (1939), 217-250.
[6] Harish-Chandra, The characters of semisimple Lie groups, Trans. Amer. Math. Soc., 83 (1956), 98-163.
[7] G. A. Hunt, A theorem of E. Cartan, Proc. Amer. Math. Soc., 7 (1956), 307-308.
[8] N. Iwahori and I. Satake, On Cartan subalgebras of a Lie algebra, Kodai Math. Sem. Rep., 3 (1950), 57-60.
[9] B. Kostant, Conjugacy of real Cartan subalgebras, Proc. Nat. Acad. Sci. U. S. A., 41 (1955), 967-970.
[10] G. D. Mostow, A new proof of E. Cartan's theorem on the topology of semisimple groups, Bull. Amer. Math. Soc., 55 (1949), 969-980.
[11] S. Murakami, Supplements and corrections to my paper: On the automorphisms of a real semisimple Lie algebra, J. Math. Soc. Japan, 5 (1953), 105-112.
[12] L. S. Pontrjagin, Continuous groups (in Russian), second edition, Moscow, 1954.
[13] H. Weyl, The structure and representations of continuous groups. The Institute for Advanced Study, Princeton, 1935.

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