On homogeneous locally nilpotent derivations of trinomial algebras

TL;DR

This paper characterizes homogeneous locally nilpotent derivations of trinomial algebra functions and describes the roots of these algebras, advancing understanding of their algebraic structure.

Contribution

It provides an explicit description of these derivations and the roots of trinomial algebras, which was not previously known.

Findings

Explicit description of homogeneous locally nilpotent derivations

Characterization of roots of trinomial algebras

Enhanced understanding of affine trinomial hypersurfaces

Abstract

We provide an explicit description of homogeneous locally nilpotent derivations of the algebra of regular functions on affine trinomial hypersurfaces. As an application, we describe the set of roots of trinomial algebras.