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Some remarks on complex Lie groups

Published online by Cambridge University Press:  22 January 2016

H. Kazama ,
D. K. Kim  and
C. Y. Oh
H. Kazama
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan
D. K. Kim
Affiliation:
Department of Mathematics, Chonbuk National University, Chonju, Chonbuk 561-756, Korea
C. Y. Oh
Affiliation:
Department of Applied Mathematics, Yosu National University, Yosu, Chollanam 550-749, Korea
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Abstract

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First we show that any complex Lie group is complete Kähler. Moreover we obtain a plurisubharmonic exhaustion function on a complex Lie group as follows. Let the real Lie algebra of a maximal compact real Lie subgroup K of a complex Lie group G. Put q := dimC Then we obtain that there exists a plurisubharmonic, strongly (q + 1)-pseudoconvex in the sense of Andreotti-Grauert and K-invariant exhaustion function on G.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 157 , 2000 , pp. 47 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[1] Andreotti, A. and Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 99 (1962), 193–259.Google Scholar
[2] Iwasawa, K., On some types of topological groups, Annals of Math., 50 (1949), 507–558.CrossRefGoogle Scholar
[3] Kazama, H., On pseudoconvexity of complex abelian Lie groups, J. Math. Soc. Japan, 25 (1973), 329–333.Google Scholar
[4] Kazama, H., On pseudoconvexity of complex Lie groups, Mem. Fac. Sci. Kyushu Univ., 27 (1973), 241–247.Google Scholar
[5] Matsushima, Y., Espaces homogènes de Stein des groupes de Lie complexes, Nagoya Math. J., 16 (1960), 205–218.CrossRefGoogle Scholar
[6] Matsushima, Y. and Morimoto, A., Sur certains espaces fibrés holomorphes sur une variété de Stein, Bull. Soc. Math. France, 88 (1960), 137–155.CrossRefGoogle Scholar
[7] Morimoto, A., Non-compact complex Lie groups without non-constant holomorphic functions, Proc. Conf. on Complex Analysis, Minneapolis (1965), 256–272.Google Scholar
[8] Morimoto, A., On the classification of non-compact complex abelian Lie groups, Trans. Amer. Math. Soc., 123 (1966), 200–228.Google Scholar
[9] Nakano, S., On the inverse of monoidal transformation, Publ.RIMS, 6 (1970), 483–502.CrossRefGoogle Scholar
[10] Takeuchi, S., On completeness of holomorphic principal bundles, Nagoya Math. J., 57 (1974), 121–138.Google Scholar