Automorphisms fixing a variable of K<x,y,z>

Details Automorphisms fixing a variable of K<x,y,z> Automorphisms fixing a variable of K<x,y,z>

2004-06-10

arxiv.org/abs/math/0406207v1

Journal of Algebra 291 (2005), No. 1, 250-258

Mathematics

Rings and Algebras

8 pages

Scientific paper

10.1016/j.jalgebra.2005.04.009

We study automorphisms of the free associative algebra K over a field K which fix z and such that the images of x, y are linear with respect to x, y. We prove that some of these automorphisms are wild in the class of all automorphisms fixing z, including the well known automorphism discovered by Anick, and show how to recognize the wild ones. This class of automorphisms induces tame automorphisms of the polynomial algebra K[x,y,z]. For n>2 the automorphisms of K which fix z and are linear in the x's are tame.

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