A Universal Approach to Vertex Algebras

TL;DR

This paper presents a universal characterization of vertex algebras using graded co-operads, offering a new algebraic framework and exploring its categorical implications.

Contribution

It introduces a novel approach to vertex algebras by describing them as algebras over a graded co-operad, expanding their theoretical understanding.

Findings

Vertex algebras characterized via graded co-operads

Examples illustrating the new framework provided

Discussion of categorical implications of the characterization

Abstract

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.