Tame and wild automorphisms of differential polynomial algebras of rank 2

Abstract

It is proved that the tame automorphism group of a differential polynomial algebra $k\{x,y\}$ over a field $k$ of characteristic $0$ in two variables $x,y$ with $m$ commuting derivations ${\delta }_1,\dots ,{\delta }_m$ is a free product with amalgamation. An example of a wild automorphism of the algebra $k\{x,y\}$ in the case of $m\ge 2$ derivations is constructed.

13 pages, in Russian