We construct a family of 3d quantum field theories $\mathcal T_ {n, k}^ A $ that conjecturally
provide a physical realization--and derived generalization--of non-semisimple mathematical …

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 …

Abstract By studying Rozansky-Witten theory with non-compact target spaces we find new
connections with knot invariants whose physical interpretation was not known. This opens …

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 …

We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming
from twist non-degenerate finite unimodular ribbon categories. Our construction produces …

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 prove that quantized multiplicative quiver varieties, quantum character varieties, and
Kauffman bracket skein algebras each define sheaves of Azumaya algebras over the …

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 unrolled quantum groups at odd roots of unity give rise to relative modular
categories. These are the main building blocks for the construction of (1+ 1+ 1)–TQFTs …

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and
prove that their categories of local modules are, again, modular. This generalizes previous …