# The Strong Anick Conjecture is true

Journal of the European Mathematical Society (2007)

- Volume: 009, Issue: 4, page 659-679
- ISSN: 1435-9855

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topDrensky, 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 -

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