On simple derivations and the group of polynomial automorphisms commuting with certain derivations

2018/08/23 by Dan Yan, Yan, Dan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1808.07612

openalex publication_date 2018/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we first study the subgroup of K-automorphisms of K[x₁,\allowbreak …,x_n] which commutes with a simple derivation of K[x₁,…,x_n]. We show that the subgroup of K-automorphisms of K[x₁,…,x_n] which commutes with a simple derivation of K[x₁,…,x_n] consists of translations under certain hypothesis. We also prove that the subgroup of K-automorphisms of K[x₁,x₂] which commutes with a simple derivation is trivial under the same hypothesis, and the subgroup of K-automorphisms of K[x₁,…,x_n] which commutes with simple Shamsuddin derivations is trivial under the same hypothesis. Then we give an affirmative answer to the conjecture proposed in \cite13 for n=2.

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