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 construct log-modular quantum groups at even order roots of unity, both as finite-
dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de …

We develop a theory of Frobenius functors for symmetric tensor categories (STC) 𝒞 over a
field 𝒌 of characteristic p, and give its applications to classification of such categories …

Several complications arise when attempting to work with fusion categories over arbitrary
fields. Here we describe some of the new phenomena that occur when the field is not …

Andrew Schopieray A diverse collection of fusion categories, in the language of [22], may be
realized by the representation theory of quantum groups. There is substantial literature …

We consider quantum group representations for a semisimple algebraic group G at a
complex root of unity q. Here q is allowed to be of any order. We revisit some fundamental …

We study the semiclassical limit κ→∞ of the generalized quantum Langlands kernel
associated to a Lie algebra g and an integer level p. This vertex algebra acquires a big …

A modular tensor category is a non-degenerate ribbon finite tensor category and a ribbon
factorizable Hopf algebra is a Hopf algebra whose finite-dimensional representations form a …

We consider quantum group representations Rep (G_q) for a semisimple algebraic group G
at a complex root of unity q. Here we allow q to be of any order. We first show that the …

We investigate the splitting property of quasitriangular Hopf algebras through the lens of
twisted tensor products. Specifically, we demonstrate that an infinite-dimensional …