The strong Anick conjecture is true

Details The strong Anick conjecture is true The strong Anick conjecture is true

2005-07-08

arxiv.org/abs/math/0507170v2

Mathematics

Rings and Algebras

25 pages, corrected typos and acknowledgements

Scientific paper

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K 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. 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. We also find a large new class of wild automorphisms of K 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.

Affiliated with

Also associated with

No associations

Rating

The strong Anick conjecture is true does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The strong Anick conjecture is true, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The strong Anick conjecture is true will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375032