We prove that the subgroup of triangular automorphisms of the complex affine n -space is maximal among all solvable subgroups of Aut ( 𝔸 ℂ n ) for every n . In particular, it is a Borel subgroup of Aut ( 𝔸 ℂ n ) , when the latter is viewed as an ind-group. In dimension two, we prove that the triangular subgroup is a maximal closed subgroup and that nevertheless, it is not maximal among all subgroups of Aut ( 𝔸 ℂ 2 ) . Given an automorphism f of 𝔸 ℂ 2 , we study the question whether the group generated by f and the triangular subgroup is equal to the whole group Aut ( 𝔸 ℂ 2 ) .