Linearity and Nonlinearity of groups of polynomial automorphisms

2022/12/05 by Olivier Mathieu, Mathieu, Olivier
Chemistry · Mathematics · #10D20 #14D20 #17B65 #Advanced Differential Equations and Dynamical Systems #Carbohydrate Chemistry and Synthesis #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2212.02460

openalex publication_date 2022/12/05 · 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. 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 K³ are nonlinear, even for a finite field K.

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