The Strong Anick Conjecture is true

Drensky, Vesselin, and Yu, Jie-Tai. "The Strong Anick Conjecture is true." Journal of the European Mathematical Society 009.4 (2007): 659-679. <http://eudml.org/doc/277384>.

@article{Drensky2007,
abstract = {Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra $K\langle x,y,z\rangle $ over a field $K$ of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of $K\langle x,y,z\rangle $. In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a similar result for several large classes of automorphisms of $K\langle x,y,z\rangle $. We also find a large new class of wild automorphisms of $K\langle x,y,z\rangle $ which is not covered by the results of Umirbaev. Finally, we study the lifting problem for automorphisms and coordinates of polynomial algebras, free metabelian algebras and free associative algebras and obtain some interesting new results.},
author = {Drensky, Vesselin, Yu, Jie-Tai},
journal = {Journal of the European Mathematical Society},
keywords = {automorphisms of free and polynomial algebras; tame automorphisms; wild automorphisms; coordinates in free algebras; automorphisms of free algebras; automorphisms of polynomial algebras; tame automorphisms; wild automorphisms, coordinates in free algebras},
language = {eng},
number = {4},
pages = {659-679},
publisher = {European Mathematical Society Publishing House},
title = {The Strong Anick Conjecture is true},
url = {http://eudml.org/doc/277384},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Drensky, Vesselin
AU - Yu, Jie-Tai
TI - The Strong Anick Conjecture is true
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 4
SP - 659
EP - 679
AB - Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra $K\langle x,y,z\rangle $ over a field $K$ of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of $K\langle x,y,z\rangle $. In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a similar result for several large classes of automorphisms of $K\langle x,y,z\rangle $. We also find a large new class of wild automorphisms of $K\langle x,y,z\rangle $ which is not covered by the results of Umirbaev. Finally, we study the lifting problem for automorphisms and coordinates of polynomial algebras, free metabelian algebras and free associative algebras and obtain some interesting new results.
LA - eng
KW - automorphisms of free and polynomial algebras; tame automorphisms; wild automorphisms; coordinates in free algebras; automorphisms of free algebras; automorphisms of polynomial algebras; tame automorphisms; wild automorphisms, coordinates in free algebras
UR - http://eudml.org/doc/277384
ER -