Linearity and Non-linearity of Groups of Polynomial Automorphisms of K²

2022/08/26 by Olivier Mathieu, Mathieu, Olivier
Mathematics · #20F29 20E36 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2208.12751

openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field, and let \Aut K² be the group of polynomial automorphisms of K². We investigate which subgroups are linear or not. In characteristic zero, there are small nonlinear subgroups and some big linear subgroups. When K has finite characteristic, the whole group \Aut K² is linear whenever K is finite, and nonlinear otherwise.

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