Related papers: Module Categories of the Generic Virasoro VOA and …

We consider two families of categories. The first is the family of semisimple quotients of H. Andersen's tilting module categories for quantum groups of Lie type $B$ specialized at odd roots of unity. The second consists of categories…

This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…

Motivated by connections to the singlet vertex operator algebra in the $\mathfrak{g}=\mathfrak{sl}_2$ case, we study the unrolled restricted quantum groups $\overline{U}_q^H(\mathfrak{g})$ at arbitrary roots of unity with a focus on its…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is…

For a simple, self-dual, strong CFT-type vertex operator algebra (VOA) of central charge $c$, we describe the Virasoro $n$-point correlation function on a genus $g$ marked Riemann surface in the Schottky uniformisation. We show that this…

In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize…

Let $G$ be a rank $n$ additive subgroup of $\bC$ and $\Vir[G]$ the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over $\Vir[G]$ are completely determined.…

We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum…

In this note we prove two main results. 1. In a rigid braided finite tensor category over C (not necessarily semisimple), some power of the Casimir element and some even power of the braiding is unipotent. 2. In a (semisimple) modular…

We construct a large family of ribbon quasi-Hopf algebras related to small quantum groups, with a factorizable R-matrix. Our main purpose is to obtain non-semisimple modular tensor categories for quantum groups at even roots of unity, where…

In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded…

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-equivariantization procedure. The existence of such quantum groups…

Let $V$ be an $\mathbb{N}$-graded, simple, self-contragredient, $C_2$-cofinite vertex operator algebra. We show that if the $S$-transformation of the character of $V$ is a linear combination of characters of $V$-modules, then the category…

The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an…

Let $A$ be a commutative algebra in a braided monoidal category $\mathcal{C}$; e.g., $A$ could be an extension of a vertex operator algebra (VOA) $V$ in a category $\mathcal{C}$ of $V$-modules. We study when the category $\mathcal{C}_A$ of…

In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum $\mathbb{A}$ in a modular fusion category $\mathcal{C}$ was introduced as part of a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In this paper,…

It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…

We construct a series of finite-dimensional quantum groups as braided Drinfeld doubles of Nichols algebras of type Super A, for an even root of unity, and classify ribbon structures for these quantum groups. Ribbon structures exist if and…

The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…