On vertex algebras and their modules associated with even lattices

TL;DR

This paper explores vertex algebras linked to even lattices, including degenerate cases, recovering known results and establishing new classifications and reducibility theorems for modules.

Contribution

It introduces a novel approach to vertex algebras from even lattices and classifies irreducible modules, extending understanding of their structure.

Findings

Classified irreducible modules for certain conditions

Established complete reducibility theorem

Recovered and extended known results on vertex algebras

Abstract

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study modules for Heisenberg algebras and we classify irreducible modules satisfying certain conditions and obtain a complete reducibility theorem.