AIMS Mathematics, 2020, 5(4): 3547-3555. doi: 10.3934/math.2020230

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On the Tame automorphisms of differential polynomial algebras

Department of Mathematics, Harran University, Şanlıurfa, Turkey

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.
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