We review briefly the existing vertex-operator-algebraic constructions of various tensor
category structures on module categories for affine Lie algebras. We discuss the results first …

For a finite-dimensional simple Lie algebra gg, we use the vertex tensor category theory of
Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra …

This is the eighth 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 show that if V is a vertex operator algebra such that all the irreducible ordinary V-
modules are C_1 C 1-cofinite and all the grading-restricted generalized Verma modules for …

Given a non-semisimple braided tensor category, with oplax tensor functors from known
braided tensor categories, we ask: How does this knowledge characterize the tensor product …

Let $\mathcal {O} _c $ be the category of finite-length central-charge-$ c $ modules for the
Virasoro Lie algebra whose composition factors are irreducible quotients of reducible Verma …

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-
positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of …

Using the tensor category theory developed by Lepowsky, Zhang and the second author, we
construct a braided tensor category structure with a twist on a semisimple category of …

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 …

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) …