On Automorphisms of the Affine Cremona Group
Annales de l'Institut Fourier, Volume 63 (2013) no. 3, p. 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 = 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 n sont des automorphismes intérieurs modulo des automorphismes du corps , 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.

DOI : https://doi.org/10.5802/aif.2785
Classification:  14R10,  14R20,  14L30
Keywords: Polynomial automorphisms, algebraic group actions, ind-varieties, affine n-space
@article{AIF_2013__63_3_1137_0,
     author = {Kraft, Hanspeter and Stampfli, Immanuel},
     title = {On Automorphisms of the Affine Cremona Group},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {3},
     year = {2013},
     pages = {1137-1148},
     doi = {10.5802/aif.2785},
     mrnumber = {3137481},
     zbl = {1297.14059},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2013__63_3_1137_0}
}
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. http://www.numdam.org/item/AIF_2013__63_3_1137_0/

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