# $6A$-Algebra and its representations

## TL;DR

This paper investigates the structure and representations of a specific vertex operator algebra called 6A-algebra, proving its uniqueness, classifying its irreducible modules, and determining its fusion rules.

## Contribution

It introduces the 6A-algebra generated by two Ising vectors, proves its VOA structure is unique, and classifies its irreducible modules and fusion rules.

## Key findings

- Uniqueness of the 6A-algebra VOA structure
- Classification of irreducible modules
- Determination of fusion rules

## Abstract

In this paper, we study the structure and representation of a $6A$-algebra which is a vertex operator algebra generated by two Ising vectors $e,f$ with inner product $\left\langle e,f\right\rangle =\frac{5}{2^{10}}.$ In particular, we prove the uniqueness of the vertex operator algebra structure of this 6A-algebra, classify the irreducible modules, and determine the fusion rules.