Complex abelian Lie groups with finite-dimensional cohomology groups

Hideaki KAZAMA; Takashi UMENO

doi:10.2969/jmsj/03610091

Hideaki KAZAMA, Takashi UMENO

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 1 Pages 91-106

DOI https://doi.org/10.2969/jmsj/03610091

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Published: 1984 Received: June 07, 1982 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) H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472.
2) H. Grauert and R. Remmert, Theorie der Steinschen Raume, Springer, Berlin-Heidelberg-New York, 1977.
3) H. Kazama, On pseudoconvexity of complex abelian Lie groups, J. Math. Soc. Japan, 25 (1973), 329-333.
4) K. Kopfermann, Maximale Untergruppen Abelscher komplexer Liescher Gruppen, Schr. Math. Inst. Univ. Münster, 29(1964).
5) B. Malgrange, Faisceaux sur des variétés analytiques réelles, Bull. Soc. Math. France 85(1957), 231-237.
6) B. Malgrange, La cohomologie dune variété analytique complexe à bord pseudo-convexe n'est pas nécessairement séparée, C. R. Acad. Sci. Paris Sér. A, 280(1975), 93-95.
7) A. Morimoto, Non-compact complex Lie groups without non-constant holomorphic functions, Proc. Conf. on Complex Analysis (Minneapolis 1964), Springer, 1965, 256-272.
8) A. Morimoto, On the classification of non-compact complex abelian Lie groups, Trans. Amer. Math. Soc., 123 (1966), 200-228.
9) J. Morrow and K. Kodaira, Complex Manifolds, Holt, Rinehart and Winston, Inc., New York, 1971.
10) R. Narasimhan, The Levi problem in the theory of functions of several complex variables, Proc. Internat. Congr. Math. (Stockholm 1962), Almgvist and Wiksells, Uppsala, 1963, 385-388.
11) P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126, Springer, 1970.

Right : [1] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472.
[2] H. Grauert and R. Remmert, Theorie der Steinschen Räume, Springer, Berlin-Heidelberg-New York, 1977.
[3] H. Kazama, On pseudoconvexity of complex abelian Lie groups, J. Math. Soc. Japan, 25 (1973), 329-333.
[4] K. Kopfermann, Maximale Untergruppen Abelscher komplexer Liescher Gruppen, Schr. Math. Inst. Univ. Münster, 29(1964).
[5] B. Malgrange, Faisceaux sur des variétés analytiques réelles, Bull. Soc. Math. France 85 (1957), 231-237.
[6] B. Malgrange, La cohomologie d'une variété analytique complexe à bord pseudo-convexe n'est pas nécessairement séparée, C. R. Acad. Sci. Paris Sér. A, 280 (1975), 93-95.
[7] A. Morimoto, Non-compact complex Lie groups without non-constant holomorphic functions, Proc. Conf. on Complex Analysis (Minneapolis 1964), Springer, 1965, 256-272.
[8] A. Morimoto, On the classification of non-compact complex abelian Lie groups, Trans. Amer. Math. Soc., 123 (1966), 200-228.
[9] J. Morrow and K. Kodaira, Complex Manifolds, Holt, Rinehart and Winston, Inc., New York, 1971.
[10] R. Narasimhan, The Levi problem in the theory of functions of several complex variables, Proc. Internat. Congr. Math. (Stockholm 1962), Almgvist and Wiksells, Uppsala, 1963, 385-388.
[11] P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126, Springer, 1970.

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