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A note on Automorphisms of the Affine Cremona Group
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 4239178
Author(s) Stampfli, Immanuel
Author(s) at UniBasel van Santen, Immanuel
Year 2013
Title A note on Automorphisms of the Affine Cremona Group
Journal Mathematical Research Letters
Volume 20
Number 6
Pages / Article-Number 1177-1181
Abstract Let G be an ind-group and let U⊆G be a unipotent ind-subgroup. We prove that an abstract group automorphism θ:G→G maps U isomorphically onto a unipotent ind-subgroup of G, provided that θ fixes a closed torus T⊆G, which normalizes U and the action of T on U by conjugation fixes only the neutral element. As an application we generalize a result by Hanspeter Kraft and the author as follows: If an abstract group automorphism of the affine Cremona group G3 in dimension 3 fixes the subgroup of tame automorphisms TG3, then it also fixes a whole family of non-tame automorphisms (including the Nagata automorphism).
Publisher International Press
ISSN/ISBN 1073-2780 ; 1945-001X
edoc-URL https://edoc.unibas.ch/59705/
Full Text on edoc No
Digital Object Identifier DOI 10.4310/MRL.2013.v20.n6.a14
ISI-Number WOS:000342635700014
Document type (ISI) Article
 
   

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