Deforming vertex algebras by vertex bialgebras

This is a continuation of a previous study initiated by one of us on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right H-comodule nonlocal vertex algebra for a nonlocal vertex bialgebraH and give a construction of deformations of vertex algebras with a right H-comodule nonlocal vertex algebra structure and a compatible H-module nonlocal vertex algebra structure. We also give a construction of φ-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.

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