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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

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