no. 3
On Automorphisms of the Affine Cremona Group
Kraft, Hanspeter1; Stampfli, Immanuel1
1 Universität Basel Mathematisches Institut Rheinsprung 21, CH-4051 Basel (Suisse)
Annales de l'Institut Fourier, Volume 63 (2013) no. 3, pp. 1137-1148.

We show that every automorphism of the group 𝒢 n :=Aut(𝔸 n ) of polynomial automorphisms of complex affine n-space 𝔸 n =ℂ n is inner up to field automorphisms when restricted to the subgroup T𝒢 n of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension n=2 where all automorphisms are tame: T𝒢 2 =𝒢 2 . The methods are different, based on arguments from algebraic group actions.

Nous montrons que tous les automorphismes du groupe des automorphismes polynomiaux de l’espace affine ℂ n sont des automorphismes intérieurs modulo des automorphismes du corps ℂ, si nous nous restreignons au sous-groupe des automorphismes modérés. Ceci généralise un résultat de Julie Déserti traitant le cas de la dimension n=2. Dans ce cas, tous les automorphismes polynomiaux sont modérés. Nos méthodes sont différentes de celles de Julie Déserti et sont basées sur des arguments d’actions de groupes algébriques.

Received:
Accepted:
DOI: 10.5802/aif.2785
Classification: 14R10, 14R20, 14L30
Keywords: Polynomial automorphisms, algebraic group actions, ind-varieties, affine n-space
Mot clés : Automorphismes polynomiaux, actions de groupes algébriques, variétés algébriques de dimension infinie, éspace affine

Kraft, Hanspeter 1; Stampfli, Immanuel 1

1 Universität Basel Mathematisches Institut Rheinsprung 21, CH-4051 Basel (Suisse) 
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Kraft, Hanspeter; Stampfli, Immanuel. On Automorphisms of the Affine Cremona Group. Annales de l'Institut Fourier, Volume 63 (2013) no. 3, pp. 1137-1148. doi : 10.5802/aif.2785. https://aif.centre-mersenne.org/articles/10.5802/aif.2785/

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