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2000 Some remarks on complex Lie groups
H. Kazama, D. K. Kim, C. Y. Oh
Nagoya Math. J. 157: 47-57 (2000).

Abstract

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 ${\frak k}$ the real Lie algebra of a maximal compact real Lie subgroup $K$ of a complex Lie group $G$. Put $q:=\dim_ {\Bbb C} {\frak k} \cap \sqrt{-1} {\frak k}$. Then we obtain that there exists a plurisubharmonic, strongly $(q + 1)$-pseudoconvex in the sense of Andreotti-Grauert and $K$-invariant exhaustion function on $G$.

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H. Kazama. D. K. Kim. C. Y. Oh. "Some remarks on complex Lie groups." Nagoya Math. J. 157 47 - 57, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0957.32010
MathSciNet: MR1752474

Subjects:
Primary: 32M05
Secondary: 32U10

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

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