Nagoya Mathematical Journal

Some remarks on complex Lie groups

H. Kazama, D. K. Kim, and C. Y. Oh

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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 ${\frak k}$ 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 $G$.

Article information

Nagoya Math. J., Volume 157 (2000), 47-57.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
Secondary: 32U10: Plurisubharmonic exhaustion functions


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

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