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 …

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 …

We show that there is a braided tensor category structure on the category of C 1-cofinite
modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central …

The vertex algebras $ V^{(p)} $ and $ R^{(p)} $ introduced in [2] are very interesting relatives
of the famous triplet algebras of logarithmic CFT. The algebra $ V^{(p)} $(respectively …

We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex
algebra A and its commutant V= Com A (U). Specifically, we assume that A≌⊕ i∈ IU i⊗ V i …

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 …

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 …

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 …

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 …

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 …