Tame and wild automorphisms of differential polynomial algebras of rank 2
Bibinur Duisengalieva, Altyngul Naurazbekova, and Ualbai Umirbaev

TL;DR
This paper investigates the structure of automorphism groups of differential polynomial algebras in two variables, proving the tame automorphisms form a free product with amalgamation and providing an example of a wild automorphism for multiple derivations.
Contribution
It establishes the algebraic structure of tame automorphisms and constructs the first known example of a wild automorphism in this context.
Findings
Tame automorphism group is a free product with amalgamation.
Existence of wild automorphisms for multiple derivations.
Structural insights into automorphism groups of differential polynomial algebras.
Abstract
It is proved that the tame automorphism group of a differential polynomial algebra over a field of characteristic in two variables with commuting derivations is a free product with amalgamation. An example of a wild automorphism of the algebra in the case of derivations is constructed.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems
