The Filtration Induced by a Locally Nilpotent Derivation

TL;DR

The paper studies filtrations from locally nilpotent derivations to classify algebraic structures and automorphisms, introducing a new method for analyzing algebra invariants and providing novel examples.

Contribution

It introduces an efficient method to recover invariants, isomorphism classes, and automorphism groups using filtrations from locally nilpotent derivations.

Findings

Method effectively recovers Makar-Limanov invariants

Classifies automorphism groups of known algebras

Provides a new class of fully describable examples

Abstract

We investigate the filtration corresponding to the degree function induced by a non-zero locally nilpotent derivations and its associated graded algebra. As an application we provide an efficient method to recover the Makar-Limanov invariants, isomorphism classes and automorphism groups of classically known algebras. We also present a new class of examples which can be fully described with this method.