Tame Automorphisms Fixing a Variable of Free Associative Algebras of   Rank Three
  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. 
Vesselin Drensky and Jie-Tai Yu