On VOAs Associated to Jordan Algebras of Type $C$

TL;DR

This paper constructs universal vertex operator algebras linked to type C Jordan algebras and establishes their simplicity, advancing the understanding of algebraic structures in conformal field theory.

Contribution

It introduces a new class of universal VOAs associated with type C Jordan algebras and proves their simplicity, which was previously unknown.

Findings

Construction of universal VOAs linked to type C Jordan algebras

Proof of the simplicity of these VOAs

Establishment of the algebraic structure connecting VOAs and Jordan algebras

Abstract

In this article, we construct certain universal VOAs whose Greiss algebras are type C Jordan algebras. We also prove the corresponding simplicity result.