Tame Automorphisms Fixing a Variable of Free Associative Algebras of Rank Three
arXiv:math/0605044
Abstract
We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix the variable z. We describe the structure of the group of z-tame automorphisms and derive algorithms which recognize z-tame automorphisms and z-tame coordinates.