PreprintCC BY-NC-SA 4.0arXiv
Tame polynomial automorphisms
Abstract
The group of polynomial automorphisms of the affine n-space is an interesting large group. A slightly simpler group is its subgroup of tame automorphisms. Natural problems about these groups include the existence of normal subgroups, the classification of finite subgroups, the Tits alternative, and the possible dynamical degrees of their elements. One method to investigate these questions is via some actions on some metric spaces, namely the coset complex and the valuation complex, that we introduce in detail. This paper is a survey focusing on the following three cases: dimension 2, dimension 3, and dimension 4 for tame automomorphism preserving a nondegenerate quadratic form.
Related
- Degree growth for tame automorphisms of an affine quadric threefold
- Infinite transitivity of tame groups of automorphisms of affine spaces
- Polynomial automorphisms of C^2 with the same equilibrium measure
- Non-archimedean and hybrid dynamics of regular polynomial automorphisms
- Functorial equivalence classes of 2-blocks of tame representation type
BibTeX
@misc{lamy2026tame,
title = {{Tame polynomial automorphisms}},
author = {Stéphane Lamy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05655},
eprint = {2609.05655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05655},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Tame polynomial automorphisms
AU - Stéphane Lamy
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05655
UR - https://arxiv.org/abs/2609.05655
AB - The group of polynomial automorphisms of the affine n-space is an interesting large group. A slightly simpler group is its subgroup of tame automorphisms. Natural problems about these groups include the existence of normal subgroups, the classification of finite subgroups, the Tits alternative, and the possible dynamical degrees of their elements. One method to investigate these questions is via some actions on some metric spaces, namely the coset complex and the valuation complex, that we introduce in detail. This paper is a survey focusing on the following three cases: dimension 2, dimension 3, and dimension 4 for tame automomorphism preserving a nondegenerate quadratic form.
ER -