Ualbai Umirbaev, Astana et MPI, Bonn :
"Tame and wild automorphisms of polynomial algebras and free associative algebras."
Résumé : 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 ring F[x,y,z] is wild, that is, it can not be decomposed into a product of elementary automorphisms. Now I will talk about further results in this direction:
1. I will describe a set of defining relations for the group of tame automorphisms of the polynomial algebra F[x,y,z];
2. I will also prove that the well-known Anick automorphism of the free associative algebra F<x,y,z> is wild.

Ce séminaire participe à l'ACM.

Voir la programmation du séminaire d'algèbre 2003-2004 et 2002-2003.