Groups of triangular automorphisms of a free associative algebra and a polynomial algebra
Group Theory
2010-07-19 v1 Rings and Algebras
Abstract
We study a structure of the group of unitriangular automorphisms of a free associative algebra and a polynomial algebra and prove that this group is a semi direct product of abelian groups. Using this decomposition we describe a structure of the lower central series and the series of derived subgroups for the group of unitriangular automorphisms and prove that every element from the derived subgroup is a commutator. In addition we prove that the group of unitriangular automorphisms of a free associative algebra of rang more than 2 is not linear and describe some two-generated subgroups from these group. Also we give a more simple system of generators for the group of tame automorphisms than the system from Umirbaev's paper.
Keywords
Cite
@article{arxiv.1007.2711,
title = {Groups of triangular automorphisms of a free associative algebra and a polynomial algebra},
author = {Valeriy G. Bardakov and Mikhail V. Neshchadim and Yury V. Sosnovsky},
journal= {arXiv preprint arXiv:1007.2711},
year = {2010}
}
Comments
19 pages