Triangular actions on \({\mathbb{C}}^ 3\)
type: Item
instance of: scholarly article
title: Triangular actions on \({\mathbb{C}}^ 3\)
zbMATH Open document ID: 0644.14018
DOI: 10.1007/BF01258660
author: Dennis M. Snow
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155289
review text: It is proved that any free triangular action of a connected linear algebraic group \(G\) on \({\mathbb{C}}^ 3\) is equivalent to the trivial action of \(G\) on \(G\times {\mathbb{C}}^ n\), \(n=3-\dim(G)\); an analogue result is proved for quasi-algebraic actions. As an application it is proved that if \(\dim (R_ u(G))\leq 3\) and \(H\) is an algebraic subgroup of \(G\) then \(G/H\) is affine iff and only if \(R_ u(H^ 0)\cap M=1\) for each reductive subgroup \(M\) of \(G\).
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 32M99
zbMATH DE Number: 4049776
zbMATH Keywords: free triangular action
zbMATH Keywords: quasi-algebraic actions
reviewed by: Alexandru Buium
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4049776