# Irregular vertex algebras

## TL;DR

This paper introduces irregular vertex algebras, extending fundamental properties like associativity and operator product expansions, and provides elementary examples to illustrate their structure.

## Contribution

It defines irregular vertex algebras and proves key properties, expanding the theoretical framework of vertex operator algebras.

## Key findings

- Irregular vertex algebras are formally introduced.
- Key properties like associativity are established for irregular cases.
- Elementary examples of irregular vertex algebras are provided.

## Abstract

We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give some elementary examples of irregular vertex operator algebras.