Upper central series for the group of unitriangular automorphisms of a free associative algebra

We study some subgroups of the group of unitriangular automorphisms U-n of a free associative algebra over a field of characteristic zero. We find the center of U-n and describe the hypercenters of U-2 and U-3. In particular, we prove that the upper central series for U-2 has infinite length. As consequence, we prove that the groups U-n are non-linear for all n >= 2.