On Commuting automorphisms of nilpotent Lie algebras

TL;DR

This paper studies the structure of commuting automorphisms in nilpotent Lie algebras with coclass up to 3, identifying when these automorphisms form a subgroup of the automorphism group.

Contribution

It provides new conditions characterizing when the set of commuting automorphisms constitutes a subgroup in nilpotent Lie algebras with low coclass.

Findings

Conditions for commuting automorphisms to form a subgroup

Classification results for coclass ≤ 3

Insights into automorphism group structure

Abstract

We investigate the commuting automorphisms of nilpotent Lie algebras $L$ with coclass $\leq 3$. Our examination exposes the conditions under which the set of commuting automorphisms of $L$ forms a subgroup within its automorphism group.