We show that the category of finite-length generalized modules for the singlet vertex algebra
M (p), p∈ Z> 1, is equal to the category OM (p) of C 1-cofinite M (p)-modules, and that this …

Let V be a simple vertex operator algebra satisfying the following conditions:(i) V (n)= 0 for
n< 0,, and the contragredient module V'is isomorphic to V as a V-module;(ii) every weak V …

Abstract Suppose V^ G VG is the fixed-point vertex operator subalgebra of a compact group
G acting on a simple abelian intertwining algebra V. We show that if all irreducible V^ G VG …

We construct two non-semisimple braided ribbon tensor categories of modules for each
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the
framework of vertex operator algebras and the application of this result to the construction of …

This is the third part in a series of papers developing a tensor product theory for modules for
a vertex operator algebra. The goal of this theory is to construct a “vertex tensor category” …

This is the first part in a series of papers developing a tensor product theory for modules for a
vertex operator algebra. The goal of this theory is to construct a “vertex tensor category” …

We show that direct limit completions of vertex tensor categories inherit vertex and braided
tensor category structures, under conditions that hold for example for all known Virasoro and …

Abstract Let V⊆ A be a conformal inclusion of vertex operator algebras and let C be a
category of grading-restricted generalized V-modules that admits the vertex algebraic …

We show that if $\mathcal {U} $ and $\mathcal {V} $ are locally finite abelian categories of
modules for vertex operator algebras $ U $ and $ V $, respectively, then the Deligne tensor …