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On the tame automorphisms of differential polynomial algebras. (English) Zbl 1484.12010

Summary: Let \(R\{x, y\}\) be the differential polynomial algebra in two differential indeterminates \(x, y\) over a differential domain \(R\) with a derivation operator \(\delta \). In this paper, we study on automorphisms of the differential polynomial algebra \(R\{x, y\}\) with one derivation operator. Using a method in group theory, we prove that the Tame subgroup of automorphism of \(R\{x, y\}\) is the amalgamated free product of the Triangular and the Affine subgroups over their intersection.

MSC:

12H05 Differential algebra
08B25 Products, amalgamated products, and other kinds of limits and colimits
16W20 Automorphisms and endomorphisms
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