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 ).