Indecomposable modules of solvable Lie algebras

TL;DR

This paper classifies all uniserial modules of a specific class of solvable Lie algebras formed by a semidirect product of an automorphism and an abelian algebra over an algebraically closed field of characteristic zero.

Contribution

It provides a complete classification of uniserial modules for solvable Lie algebras constructed as semidirect products with an automorphism.

Findings

Complete classification of uniserial modules

Applicable to Lie algebras over algebraically closed fields of characteristic zero

Framework for understanding module structure in solvable Lie algebras

Abstract

We classify all uniserial modules of the solvable Lie algebra $\mathfrak{g}=\langle x\rangle \ltimes V$, where $V$ is an abelian Lie algebra over an algebraically closed field of characteristic 0 and $x$ is an arbitrary automorphism of $V$.