2020/11/12 by Shoya Yasuda, Yasuda, Shoya
Biochemistry, Genetics and Molecular Biology · Mathematics · #14R10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Microtubule and mitosis dynamics
paper · pdf · doi:10.48550/arxiv.2011.06311
openalex publication_date 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An automorphism F of the polynomial ring in n variables over a field of characteristic zero is said to be \it co-tame if the subgroup of the automorphism group of the polynomial ring generated by F and affine automorphisms contains the tame subgroup. There exist many examples of such an F, and several sufficient conditions for co-tameness are already known. In 2015, Edo-Lewis gave the first example of a non-cotame automorphism, which is a tame automorphism of the polynomial ring in three variables. In this paper, we give the first example of a non-cotame automorphism which is not tame. We construct such an example when n=3 as the exponential automorphism of a locally nilpotent derivation of rank three.