Open AccessTame and Wild Coordinates of 𝐾[𝑧][𝑥,𝑦]
Author(s) -
Vesselin Drensky,
Jie-Tai Yu
Publication year - 2000
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-00-02617-9
Subject(s) - algorithm , bracket , annotation , artificial intelligence , type (biology) , computer science , mathematics , geology , paleontology , mechanical engineering , engineering
Let K be a field of characteristic zero. We characterize coordinates and tame coordinates in K[z][x, y], i.e. the images of x respectively under all automorphisms and under the tame automorphisms of K[z][x; y]. We also construct a new large class of wild automorphisms of K[z][x; y] which maps x to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, i.e. becomes tame when we extend its automorphisms to automorphisms of K[z][x, y, t].published_or_final_versio