Constructions of Vertex Operator Coalgebras via Vertex Operator Algebras

The duality between vertex operator algebras and coalgebras, modules and comodules

We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corresponding comodule structures, as well as when various comodules carry module structure.

Vertex Coalgebras, Comodules, Cocommutativity and Coassociativity

We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, D∗, which hold on vertex coalgebras. The former two properties require grading. We then discuss comodule structure. We conclude by discussing instances where graded vertex coalgebras appear, particularly a...

Constructions of Vertex Operator Coalgebras Viavertex Operator Algebraskeith

Two constructions of grading-restricted vertex (super)algebras

We give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This construction is based on a new definition of vertex operators and a new method. Our second construction is a generalization of the author’s construction of the moon...

The Notion of Vertex Operator Coalgebra and a Geometric Interpretation

The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures meromorphically induced by conformal equivalence classes of worldsheets. We then show this category is isomorphic to the category of vertex operator coalgebras...