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

Valeriy G. Bardakov; Mikhail V. Neshchadim

paper

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

arXiv:1405.6288

Abstract

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 $n \geq 2$ .

arXiv comment14 pages