Non-Noetherian generalized Heisenberg algebras

TL;DR

This paper classifies non-Noetherian generalized Heisenberg algebras, analyzing their derivations and automorphisms, especially when the defining polynomial has degree greater than one.

Contribution

It provides a complete classification of these algebras, including derivations and automorphism groups, extending previous work on their structure.

Findings

Classified non-Noetherian generalized Heisenberg algebras

Determined all locally finite and locally nilpotent derivations for degree > 1

Described the automorphism groups of these algebras

Abstract

In this note we classify the non-Noetherian generalized Heisenberg algebras H(f) introduced by Rencai L\"u and Kaiming Zhao [Linear Algebra Appl., 2015]. In case the polynomial f has degree greater than 1, we determine all locally finite and also all locally nilpotent derivations of H(f) and describe the automorphism group of these algebras.