2010/07/16 by Valeriy G. Bardakov, М. В. Нещадим, Mikhail V. Neshchadim +4
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Group Theory (math.GR) #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.GR #math.RA
paper · pdf · doi:10.48550/arxiv.1007.2711
19 pages
arxiv created 2010/07/16 · openalex publication_date 2010/07/16 · arxiv updated 2010/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.