A new co-tame automorphism of the polynomial ring
Abstract
In this paper, we discuss subgroups of the automorphism group of the polynomial ring in n variables over a field of characteristic zero. An automorphism F is said to be co-tame if the subgroup generated by F and affine automorphisms contains the tame subgroup. In 2017, Edo-Lewis gave a sufficient condition for co-tameness of automorphisms. Let EL(n) be the set of all automorphisms satisfying Edo-Lewis's condition. Then, for a certain topology on the automorphism group of the polynomial ring, any element of the closure of EL(n) is co-tame. Moreover, all the co-tame automorphisms previously known belong to the closure of EL(n). In this paper, we give the first example of co-tame automorphisms in n variables which do not belong to the closure of EL(n).
Cite
@article{arxiv.2007.03429,
title = {A new co-tame automorphism of the polynomial ring},
author = {Shoya Yasuda},
journal= {arXiv preprint arXiv:2007.03429},
year = {2021}
}
Comments
15 pages, no figure