On the intransitive Lie algebras whose transitive parts are infinite and primitive

Tohru MORIMOTO

doi:10.2969/jmsj/02910035

Tohru MORIMOTO

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1977 Volume 29 Issue 1 Pages 35-65

DOI https://doi.org/10.2969/jmsj/02910035

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Published: 1977 Received: June 30, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Cartan, Sur la structure des groupes infinis de transformations, Ann. Ecole Norm. Sup., 21 (1904), 153-206 and 22 (1905), 219-308.
2) E. Cartan, Les sous-groupes des groupes continus de transformations, Ann. Ecole Norm. Sup., 25 (1908) 57-194.
3) E. Cartan, Les groupes de transformations continus, infinis, simples, Ann. Ecole Norm. Sup., 26 (1909), 93-161.
4) E. Cartan, La structure des groupes infinis, Seminaire de Math., exposes G et H, 1^er et 15 mars 1937.
5) V. Guillemin and S. Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc., 70 (1964), 16-47.
6) V. Guillemin, D. Quillen and S. Sternberg, The classification of the complex primitive infinite pseudogroups, Proc. Nat. Acad. Sci. U.S.A., 55 (1966), 687-690.
7) V. Guillemin, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Differential Geometry, 2 (1968), 313-345.
8) S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures, III and IV, J. Math. Mech., 14 (1965), 679-706 and 15 (1966), 163-175.
9) M. Kuranishi, On the local theory of continuous infinite pseudogroups, I and II, Nagoya Math. J., 15 (1959), 225-260 and 19 (1961), 55-91.
10) T. Morimoto and N. Tanaka, The classification of the real primitive infinite Lie algebras, J. Math. Kyoto Univ., 10 (1970), 207-243.
11) T. Morimoto, The derivation algebras of the classical infinite Lie algebras, J. Math. Kyoto Univ., 16 (1976), 1-24.
12) T. Nagano, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan, 18 (1966), 398-404.
13) I. M. Singer and S. Sternberg, On the infinite groups of Lie and Cartan, Part 1 (The transitive groups), J. Analyse Math., 15 (1965), 1-114.
14) N. Tanaka, Intransitive infinite Lie groups and generalized G-structures (unpublished).
15) K. Ueno, A study on the equivalence of generalized G-structures, M. Sc. thesis, Kyoto University, 1968.
16) H. Weyl, The classical groups, their invariants and representations, Princeton Math. Ser. No. 1, 1939.

Right : [1] E. Cartan, Sur la structure des groupes infinis de transformations, Ann. Ecole Norm. Sup., 21 (1904), 153-206 and 22 (1905), 219-308.
[2] E. Cartan, Les sous-groupes des groupes continus de transformations, Ann. Ecole Norm. Sup., 25 (1908) 57-194.
[3] E. Cartan, Les groupes de transformations continus, infinis, simples, Ann. Ecole Norm. Sup., 26 (1909), 93-161.
[4] E. Cartan, La structure des groupes infinis, Seminaire de Math., exposes G et H, 1^er et 15 mars 1937.
[5] V. Guillemin and S. Sternberg, An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc., 70 (1964), 16-47.
[6] V. Guillemin, D. Quillen and S. Sternberg, The classification of the complex primitive infinite pseudogroups, Proc. Nat. Acad. Sci. U. S. A., 55 (1966), 687-690.
[7] V. Guillemin, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Differential Geometry, 2 (1968), 313-345.
[8] S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures, III and IV, J. Math. Mech., 14 (1965), 679-706 and 15 (1966), 163-175.
[9] M. Kuranishi, On the local theory of continuous infinite pseudogroups, I and II, Nagoya Math. J., 15 (1959), 225-260 and 19 (1961), 55-91.
[10] T. Morimoto and N. Tanaka, The classification of the real primitive infinite Lie algebras, J. Math. Kyoto Univ., 10 (1970), 207-243.
[11] T. Morimoto, The derivation algebras of the classical infinite Lie algebras, J. Math. Kyoto Univ., 16 (1976), 1-24.
[12] T. Nagano, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan, 18 (1966), 398-404.
[13] I. M. Singer and S. Sternberg, On the infinite groups of Lie and Cartan, Part 1 (The transitive groups), J. Analyse Math., 15 (1965), 1-114.
[14] N. Tanaka, Intransitive infinite Lie groups and generalized G-structures (unpublished).
[15] K. Ueno, A study on the equivalence of generalized G-structures, M. Sc. thesis, Kyoto University, 1968.
[16] H. Weyl, The classical groups, their invariants and representations, Princeton Math. Ser. No. 1, 1939.

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