We show that every automorphism of the group of polynomial automorphisms of complex affine -space is inner up to field automorphisms when restricted to the subgroup of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension where all automorphisms are tame: . 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 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 . 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.
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
@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}, pages = {1137--1148}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {3}, year = {2013}, doi = {10.5802/aif.2785}, zbl = {1297.14059}, mrnumber = {3137481}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2785/} }
TY - JOUR AU - Kraft, Hanspeter AU - Stampfli, Immanuel TI - On Automorphisms of the Affine Cremona Group JO - Annales de l'Institut Fourier PY - 2013 SP - 1137 EP - 1148 VL - 63 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2785/ DO - 10.5802/aif.2785 LA - en ID - AIF_2013__63_3_1137_0 ER -
%0 Journal Article %A Kraft, Hanspeter %A Stampfli, Immanuel %T On Automorphisms of the Affine Cremona Group %J Annales de l'Institut Fourier %D 2013 %P 1137-1148 %V 63 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2785/ %R 10.5802/aif.2785 %G en %F 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/articles/10.5802/aif.2785/
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