We prove the conjecture of Gaiotto and Rap\v {c}\'ak that the $ Y $-algebras $ Y_ {L, M,
N}[\psi] $ with one of the parameters $ L, M, N $ zero, are simple one-parameter quotients of …

Let $ V $ be a vertex operator algebra with a category $\mathcal {C} $ of (generalized)
modules that has vertex tensor category structure, and thus braided tensor category …

Trialities of W-algebras are isomorphisms between the affine cosets of three different W-
(super) algebras, and were first conjectured in the physics literature by Gaiotto and Rapčák …

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H
and let C= Com (H; V) be the coset of H in V. Assuming that the module categories of interest …

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 establish rigid tensor category structure on finitely-generated weight modules for the
subregular W-algebras of sl n at levels-n+ nn+ 1 (the B n+ 1-algebras of Creutzig–Ridout …

We relate commutative algebras in braided tensor categories to braid-reversed tensor
equivalences, motivated by vertex algebra representation theory. First, for C a braided …

We study the embeddings of the simple admissible affine vertex algebras V_k (sl (2)) V k (sl
(2)) and V_k (osp (1, 2)) V k (osp (1, 2)), k ∉\mathbb Z _ ≥ 0 k∉ Z≥ 0, into the tensor …

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 …

Let $\mathcal {U} $ be a braided tensor category, typically unknown, complicated and in
particular non-semisimple. We characterize $\mathcal {U} $ under the assumption that there …