On complete reducibility for infinite-dimensional Lie algebras

TL;DR

This paper explores the conditions under which representations of infinite-dimensional Lie algebras can be decomposed into simpler components, using the framework of vertex algebra theory.

Contribution

It introduces a novel approach connecting infinite-dimensional Lie algebra representations with vertex algebra techniques for analyzing reducibility.

Findings

Established criteria for complete reducibility in this context

Linked Lie algebra representations to vertex algebra structures

Provided new insights into the structure of infinite-dimensional modules

Abstract

In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.