Vertex [formula omitted]-algebras and their [formula omitted]-coordinated modules

Abstract

In this paper, for every one-dimensional formal group F we formulate and study a notion of vertex F -algebra and a notion of ϕ -coordinated module for a vertex F -algebra where ϕ is what we call an associate of F . In the case that F is the additive formal group, vertex F -algebras are exactly ordinary vertex algebras. We give a canonical isomorphism between the category of vertex F -algebras and the category of ordinary vertex algebras. Meanwhile, for every formal group we completely determine its associates. We also study ϕ -coordinated modules for a general vertex Z -graded algebra V with ϕ specialized to a particular associate of the additive formal group and we give a canonical connection between V -modules and ϕ -coordinate modules for a vertex algebra obtained from V by Zhu’s change-of-variables theorem.