New stably tame automorphisms of polynomial algebras
type: Item
instance of: scholarly article
title: New stably tame automorphisms of polynomial algebras
zbMATH Open document ID: 0954.16023
author: Vesselin Drensky
author: Dimitre Stefanov
author: Arno van den Essen
published in: Journal of Algebra
publication date: 2000-11-09T00:00:00Z
review text: The paper under review deals with automorphisms of (commutative) polynomial algebras. Suppose \(K[X,Y]\) is the polynomial algebra in \(n\) variables \(X\) and \(m\) variables \(Y\) over a field \(K\) of characteristic 0. The authors consider an appropriate locally nilpotent derivation \(\delta\) of \(K[X,Y]\). It is defined as \(\delta(y_i)=0\) for all \(i\), and it is a \(K[Y]\)-affine transformation over the free \(K[Y]\)-module with free generators \(x_1,\dots,x_n\). The main result of the paper states that for \(w\in\ker(\delta)\) the automorphism \(\exp(w\delta)\) is stably tame. (Recall that an automorphism \(\phi\) is stably tame for \(K[X]\) if its extension to \(K[X,X_1]\) for some finite set of variables \(X_1\) is tame. Here the extension of \(\phi\) acts as \(\phi\) on \(K[X]\) and fixes the variables in \(X_1\).) Further the authors give an algorithm for constructing stably tame automorphisms, and investigate the stable tameness of some known automorphisms.
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1441827
zbMATH Keywords: automorphisms of polynomial algebras
zbMATH Keywords: stable tameness
zbMATH Keywords: stably tame automorphisms
zbMATH Keywords: locally nilpotent derivations
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: jabr.1999.8224
OpenAlex ID: W2049153741
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DOI: 10.1006/JABR.1999.8224
description: scientific article; zbMATH DE number 1441827