Generalized Vertex Algebras Generated by Parafermion-Like Vertex Operators

It is proved that for any vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of Dong and Lepowsky with W as a natural module. As an application, generalized vertex algebras are constructed from the Lepowsky–Wilson Z-algebras of any nonzero level.