# Locally nilpotent sets of derivations

## TL;DR

This paper investigates the properties of locally nilpotent sets of derivations on an algebra, exploring their structure and implications for Lie subalgebras composed of such derivations.

## Contribution

It introduces the concept of locally nilpotent sets of derivations and examines their fundamental properties and structural consequences.

## Key findings

- Established basic results about locally nilpotent sets
- Analyzed conditions under which Lie subalgebras of locally nilpotent derivations are nilpotent
- Explored implications for the structure of derivation Lie algebras

## Abstract

Let B be an algebra over a field k and let Der(B) be the set of k-derivations from B to B. We define what it means for a subset of Der(B) to be a locally nilpotent set. We prove some basic results about that notion and explore the following questions. Let L be a Lie subalgebra of Der(B); if every element of L is a locally nilpotent derivation then does it follow that L is a locally nilpotent set? Does it follow that L is a nilpotent Lie algebra?