Hopf action on vertex algebras

TL;DR

This paper investigates how Hopf algebra actions influence vertex algebras, showing that the smash product forms an $ ext{S}$-local vertex algebra but not a vertex algebra, and extends these concepts to quantum vertex algebras.

Contribution

It demonstrates the properties of Hopf actions on vertex algebras and extends $ ext{S}$-locality to quantum vertex algebras, clarifying their algebraic structure.

Findings

$V#H$ is an $ ext{S}$-local vertex algebra.

$V#H$ is not a vertex algebra when $V$ is an $H$-module vertex algebra.

$ ext{S}$-locality extends to quantum vertex algebras.

Abstract

In present paper, some properties of Hopf action on vertex algebras will be given. We prove that $V#H$ is an $\mathcal{S}$-local vertex algebra but it is not a vertex algebra when $V$ is an $H$-module vertex algebra. In addition, we extend the $\mathcal{S}$-locality to the quantum vertex algebras.