Tame and wild automorphisms of polynomial algebras and free associative algebras
by
Ualbai Umirbaev
Eurasian National University, Astana, Kazakhstan

Let F be a field of characteristic 0. It was proved by I.Shestakov and U.Umirbaev that the well-known Nagata automorphism of the polynomial algebra F[x, y, z] is wild, that is, it cannot be decomposed into a product of elementary automorphisms. Now I have proved further results in this direction: 1) I described a set of defining relations for the group of tame automorphisms of the polynomial algebra F[x, y, z]; 2) I proved that the well-known Anick automorphism of the free associative algebra F<x, y, z> is wild.

Date received: February 13, 2005