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On Automorphisms of the Affine Cremona Group

Hanspeter KraftImmanuel Stampfli — 2013

Annales de l’institut Fourier

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

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