Representability of the automorphism group of finitely generated vertex algebras

TL;DR

This paper investigates the automorphism groups of finitely generated vertex algebras, proving they are affine group schemes over noetherian rings, with implications for algebraic structure understanding.

Contribution

It establishes that automorphism groups of finitely generated vertex algebras are affine group schemes, extending the algebraic understanding of these automorphisms.

Findings

Automorphism groups are affine group schemes over noetherian rings.

The study applies to free algebras with multiple composition laws.

Provides new insights into the structure of vertex algebra automorphisms.

Abstract

We study the automorphism groups attached to a free algebra with multiple, possibly infinitely many, composition laws. As an application, we prove that the automorphism group of finitely generated vertex algebras over noetherian rings are affine group schemes.