The tame and the wild automorphisms of polynomial rings in three variables

Abstract

A characterization of tame automorphisms of the algebra A = F [ x 1 , x 2 , x 3 ] A=F[x_1,x_2,x_3] of polynomials in three variables over a field F F of characteristic 0 0 is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of A A are algorithmically recognizable.