Coordinates and automorphisms of polynomial and free associative algebras of rank three

Abstract

We study z-automorphisms of the polynomial algebra K[x, y, z] and the free associative algebra K 〈x, y, z〉 over a field K, i.e., automorphisms that fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For K 〈x, y, z〉 we include also results about the structure of the z-tame automorphisms and algorithms that recognize z-tame automorphisms and z-tame coordinates.

Keywords

automorphisms of free and polynomial algebras / tame automorphisms / wild automorphisms / coordinates / primitive elements in free algebras

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