Towards a Lie theory for vertex and conformal algebras

Abstract

We introduce several definitions within the framework ofvertex and conformal algebras which are analogous to some importantconcepts of the classical Lie theory. Most importantly, we define vertexmanifolds, which correspond to the notion of Lie groups. We provesuitable vertex/conformal versions of a number of classical results suchas the Milnor-Moore theorem, Cartier duality, and Lie's third theoremfor nilpotent Lie algebras.