On the Tame automorphisms of differential polynomial algebras

Abstract

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.

Keywords

• differential algebras
• differential polynomial algebras
• derivations
• tame automorphisms
• amalgamated product