an:01443786
Zbl 0957.32010
Kazama, H.; Kim, D. K.; Oh, C. Y.
Some remarks on complex Lie groups
EN
Nagoya Math. J. 157, 47-57 (2000).
00063832
2000
j
32M05 32U10 32F10
complete K??hler metric; complex Lie group; plurisubharmonic exhaustion function
Two main results are shown in this paper. First it is shown that there exists a complete K??hler metric on any complex Lie group. Second one obtains a plurisubharmonic exhaustion function on any complex Lie group as follows. Let \(k\) the real Lie algebra of a maximal compact real Lie subgroup \(K\) of a complex Lie group \(G\). Put \(q:=\dim_\mathbb{C} k\cap \sqrt{-1}k\). Then one obtains a plurisubharmonic, strongly \((q+1)\)-pseudoconvex -- in the sense of Andreotti-Grauert -- and \(K\)-invariant exhaustion function on \(G\), using an integral method with respect to Haar measure on \(G\).
H.Kazama (Fukuoka)