SAut_k(A^2) is simple as an infinite-dimensional algebraic group over any infinite field k; closed normal subgroups of SAut_k(A^n) contain all tame automorphisms.
Conjugacy classes of special automorphisms of the affine spaces
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Topological simplicity of the group of automorphisms of the affine plane
SAut_k(A^2) is simple as an infinite-dimensional algebraic group over any infinite field k; closed normal subgroups of SAut_k(A^n) contain all tame automorphisms.