Graded automorphisms of the algebra of polynomials in three variables

TL;DR

This paper constructs a system of automorphisms for a graded polynomial algebra in three variables, preserving the grading structure, advancing understanding of symmetries in algebraic systems.

Contribution

It introduces a new set of automorphisms that generate the automorphism group of the graded polynomial algebra in three variables, preserving the grading.

Findings

Automorphisms preserve the grading structure.

The system generates the entire automorphism group.

Provides a framework for understanding symmetries in graded polynomial algebras.

Abstract

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.