Multiplicity-Free Representations of Divergence-Free Lie Algebras

TL;DR

This paper classifies all irreducible and indecomposable multiplicity-free modules of generalized divergence-free Lie algebras, advancing understanding of their representation theory.

Contribution

It provides a complete classification of multiplicity-free modules for a broad class of divergence-free Lie algebras, extending prior work on their representations.

Findings

Classified all irreducible modules of the generalized divergence-free Lie algebras.

Identified indecomposable multiplicity-free modules within this class.

Enhanced understanding of the structure and representations of divergence-free Lie algebras.

Abstract

Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are Lie algebras of volume-preserving transformation groups. They are simple in generic case. Dokovic and Zhao found a certain graded generalization of them. In this paper, we classify all the irreducible and indecomposable multiplicity-free modules of the simple generalized divergence-free Lie algebras.