Linearity and Nonlinearity of groups of polynomial automorphisms

Olivier Mathieu

Linearity and Nonlinearity of groups of polynomial automorphisms

Group Theory 2022-12-06 v1 Commutative Algebra

Authors: Olivier Mathieu

Abstract

Let $K$ be a field, and let $\Aut \,K^2$ be the group of polynomial automorphisms of $K^2$ . If $K$ is infinite, this group is nonlinear. Moreover it contains nonlinear FG subgroups when $\ch\,K=0$ . On the opposite, it contains some linear "finite codimension" subgroups. This phenomenon is specific to dimension two: it is also proved that "finite codimension" subgroups of $\Aut\,K^3$ are nonlinear, even for a finite field $K$ .

Keywords

polynomial automorphisms linear groups nonlinear groups finite codimension subgroups field characteristic dimension two automorphism groups

Cite

@article{arxiv.2212.02460,
  title  = {Linearity and Nonlinearity of groups of polynomial automorphisms},
  author = {Olivier Mathieu},
  journal= {arXiv preprint arXiv:2212.02460},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2208.12751

Linearity and Nonlinearity of groups of polynomial automorphisms

Abstract

Keywords

Cite

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