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arXiv · 2212.02460

Linearity and Nonlinearity of groups of polynomial automorphisms

Olivier Mathieu
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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 $K$.

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Olivier Mathieu. 2022-12-05. Linearity and Nonlinearity of groups of polynomial automorphisms. https://arxiv.org/abs/2212.02460

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