Characterization of rank two locally nilpotent derivations in dimension three

TL;DR

This paper presents an algorithmic approach to characterize and compute the rank of rank two locally nilpotent derivations in three-dimensional algebraic structures, including a method for determining the plinth ideal.

Contribution

It introduces a novel algorithmic characterization and a method for computing the rank and plinth ideal of locally nilpotent derivations in three dimensions.

Findings

Algorithm for characterizing rank two locally nilpotent derivations

Method for computing the plinth ideal

Procedure for determining the rank of derivations

Abstract

In this paper we give an algorithmic characterization of rank two locally nilpotent derivations in dimension three. Together with an algorithm for computing the plinth ideal, this gives a method for computing the rank of a locally nilpotent derivation in dimension three.