On the holomorphic separability of discrete quotients of complex Lie groups
type: Item
instance of: scholarly article
title: On the holomorphic separability of discrete quotients of complex Lie groups
zbMATH Open document ID: 0766.32025
DOI: 10.1007/BF02571450
author: Karl Oeljeklaus
published in: Mathematische Zeitschrift
publication date: 1993-03-07T00:00:00Z
full work available at URL: https://eudml.org/doc/174463
review text: This article presents two examples. The first is a 4-dimensional complex homogeneous space \(X=G/\Gamma\) where \(\Gamma\) is a discrete subgroup of a connected complex Lie group \(G\). The author shows that there are enough holomorphic functions on \(X\) to separate points but that \(X\) cannot be imbedded as a closed submanifold of \(\mathbb{C}^ n\) (\(X\) is not Stein). The second is an 8-dimensional Stein manifold that has a holomorphic \(SL(2,\mathbb{R})\)-action such that the algebra of \(SL(2,\mathbb{R})\)-invariant functions is not isomorphic to the algebra of holomorphic functions on a Stein space. This is contrary to the situation for complex reductive Lie groups or compact Lie groups acting holomorphically on Stein spaces.
reviewed by: Dennis M. Snow
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 22E10
zbMATH DE Number: 126417
zbMATH Keywords: 4-dimensional complex homogeneous space
zbMATH Keywords: 8-dimensional Stein manifold
Wikidata QID: Q115391987
MaRDI profile type: Publication
cites work: Invariante holomorphe Funktionen auf reduktiven Liegruppen
cites work: Geometric invariant theory on Stein spaces
cites work: On holomorphically separable complex solv-manifolds
cites work: Quotient varieties
cites work: Espaces Homogènes De Stein Des Groupes De Lie Complexes
cites work: Sur certains espaces fibrés holomorphes sur une variété de Stein
cites work: Reductive group actions on Stein spaces
OpenAlex ID: W2093102607
description: scientific article; zbMATH DE number 126417