Formal vertex laws associated to Lie conformal algebras

Abstract

We introduce several definitions within the framework of vertex and conformal algebras that are analogous to some important concepts of the classical Lie theory. Most importantly, we define formal vertex laws, which correspond to the notion of formal group laws. We prove suitable vertex/conformal versions of a number of classical results, such as the Milnor–Moore theorem, Cartier duality, and the equivalence between formal group laws and Lie algebras.