On Automorphisms of the Affine Cremona Group

We show that every automorphism of the group $$\mathcal{G}$_n:= $\text{Aut}$($\mathbb{A}$^n)$ofpolynomialautomorphismsofcomplexaffine$n$-space$$\mathbb{A}$^n=$\mathbb{C}$^n$ is inner up to field automorphisms when restricted to the subgroup $T{\mathcal{G}}_n$ of tame automorphisms. This generalizes a result of $\text{textsc}JulieDeserti$ who proved this in dimension $n=2$ where all automorphisms are tame: $T{\mathcal{G}}_2={\mathcal{G}}_2$.