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” …

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” …

We generalize the tensor product theory for modules for a vertex operator algebra previously
developed in a series of papers by the first two authors to suitable module categories for …

This is the first part in a series of papers in which we introduce and develop a natural,
general tensor category theory for suitable module categories for a vertex (operator) …

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 …

A theory of tensor products of modules for a vertex operator algebra is being developed by
Lepowsky and the author. To use this theory, one first has to verify that the vertex operator …

This is the second part in a series of papers presenting a theory of tensor products for
module categories for a vertex operator algebra. In Part I, the notions of P (z)-and Q (z) …

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its
module category has a natural vertex tensor category structure, and consequently, a natural …

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 …

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 …