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arXiv · 1007.2711

Groups of triangular automorphisms of a free associative algebra and a polynomial algebra

Valeriy G. Bardakov·Mikhail V. Neshchadim·Yury V. Sosnovsky
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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.

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Valeriy G. Bardakov, Mikhail V. Neshchadim, Yury V. Sosnovsky. 2010-07-16. Groups of triangular automorphisms of a free associative algebra and a polynomial algebra. https://arxiv.org/abs/1007.2711

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