Deforming vertex algebras by vertex bialgebras

Abstract

This is a continuation of a previous study initiated by the third author on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right [Formula: see text]-comodule nonlocal vertex algebra for a nonlocal vertex bialgebra [Formula: see text] and give a construction of deformations of vertex algebras with a right [Formula: see text]-comodule nonlocal vertex algebra structure and a compatible [Formula: see text]-module nonlocal vertex algebra structure. We also give a construction of [Formula: see text]-coordinated quasi modules for smash product nonlocal vertex algebras. As an example, we give a family of quantum vertex algebras by deforming the vertex algebras associated to non-degenerate even lattices.