On the Tame automorphisms of differential polynomial algebras

Zehra Velioǧlu; Mukaddes Balçik; Zehra Velioǧlu; Mukaddes Balçik

doi:10.3934/math.2020230

AIMS Mathematics

2020, Volume 5, Issue 4: 3547-3555. doi: 10.3934/math.2020230

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Research article

On the Tame automorphisms of differential polynomial algebras

Zehra Velioǧlu ^,,
Mukaddes Balçik

Department of Mathematics, Harran University, Şanlıurfa, Turkey

Received: 25 February 2020 Accepted: 07 April 2020 Published: 10 April 2020
MSC : 08B25, 12H05, 16W20

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.
- differential algebras,
- differential polynomial algebras,
- derivations,
- Tame automorphisms,
- amalgamated product
Citation: Zehra Velioǧlu, Mukaddes Balçik. On the Tame automorphisms of differential polynomial algebras[J]. AIMS Mathematics, 2020, 5(4): 3547-3555. doi: 10.3934/math.2020230

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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.

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