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- W4327525023 abstract "Given a field $K$, we investigate which subgroups of the group Aut$mathbb{A}^2_K$ of polynomial automorphisms of the plane are linear or not. The results are contrasted. The group Aut$mathbb{A}^2_K$ itself is nonlinear, except if $K$ is finite, but it contains some large finite-codimensional subgroups which are linear. This phenomenon is specific to dimension two: it is easy to prove that any finite-codimensional subgroup of Aut$mathbb{A}^3_K$ is nonlinear, even for a finite field $K$. When ch$K = 0$, we also look at a similar questions for f.g. subgroups, and the results are again disparate. The group Aut$mathbb{A}^2_K$ has a one-related f.g. subgroup which is not linear. However, there is a large subgroup, of co-dimension-three, which is locally linear but not linear. This paper is respectfully dedicated to the memory of Jacques Tits." @default.
- W4327525023 created "2023-03-17" @default.
- W4327525023 creator A5051870380 @default.
- W4327525023 date "2022-12-05" @default.
- W4327525023 modified "2023-09-30" @default.
- W4327525023 title "Linearity and Nonlinearity of Groups of Polynomial Automorphisms of the Plane" @default.
- W4327525023 hasPublicationYear "2022" @default.
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