Stein quotients of connected complex Lie groups
type: Item
instance of: scholarly article
title: Stein quotients of connected complex Lie groups
zbMATH Open document ID: 0582.32020
DOI: 10.1007/BF01168831
author: Dennis M. Snow
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155054
review text: Let G be a connected complex Lie group and H a closed, connected complex Lie subgroup of G. The author investigates the conditions for the quotient complex manifold \(X=G/H\) to be a Stein manifold, in terms of various algebraic and geometric properties of the groups G and H. If G acts effectively on X, we know that H has a semi-direct product decomposition \(H=L\cdot V\), where L is a maximal reductive subgroup of H and V is a simply connected normal solvable subgroup of H. The author first asserts that if \(X=G/H\) is a Stein manifold, then \(V\cap M=\{e\}\) for every maximal reductive subgroup M of G. The author conjectures that the above condition is also sufficient for X to be Stein. In fact, the author proves, among other things, that this is true for solvable G.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E10
zbMATH DE Number: 3931390
zbMATH Keywords: connected complex Lie group
zbMATH Keywords: Stein manifold
Wikidata QID: Q115393966
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3931390