This is the sixth 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) …

Motivated by connections to the singlet vertex operator algebra in the $\mathfrak
{g}=\mathfrak {sl} _2 $ case, we study the unrolled restricted quantum groups $\overline {U} …

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 …

0. Introduction. The category of finite direct sums of standard (integrable highest weight)
modules of a fixed positive integral level k for an affine Lie algebra ˆg is particularly …

We provide a ribbon tensor equivalence between the representation category of small
quantum SL. 2/, at parameter q D ei= p, and the representation category of the triplet vertex …

The notion of the genus of a quadratic form is generalized to vertex operator algebras. We
define it as the modular braided tensor category associated to a suitable vertex operator …

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 …

This is the fourth 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) …

We describe a logarithmic tensor product theory for certain module categories for a"
conformal vertex algebra". In this theory, which is a natural, although intricate, generalization …

A general method for constructing logarithmic modules in vertex operator algebra theory is
presented. By utilizing this approach, we give explicit vertex operator construction of certain …