Hopf actions on vertex algebras

In this article, we investigate Hopf actions on vertex algebras. Our first main result is that every finite-dimensional Hopf algebra that inner faithfully acts on a given π_2-injective vertex algebra must be a group algebra. Secondly, under suitable assumptions, we establish a Schur-Weyl type duality for semisimple Hopf actions on Hopf modules of vertex algebras.