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A note on Automorphisms of the Affine Cremona Group

Stampfli, Immanuel. (2013) A note on Automorphisms of the Affine Cremona Group. Mathematical Research Letters, 20 (6). pp. 1177-1181.

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Official URL: https://edoc.unibas.ch/59705/

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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).
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc)
UniBasel Contributors:van Santen, Immanuel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:International Press
ISSN:1073-2780
e-ISSN:1945-001X
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:02 Feb 2018 10:08
Deposited On:02 Feb 2018 10:08

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