Related papers: Fusion Rings over Drinfeld Doubles

We consider generalized Haagerup categories such that $1 \oplus X$ admits a $Q$-system for every non-invertible simple object $X$. We show that in such a category, the group of order two invertible objects has size at most four. We describe…

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…

We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid $\mathbb N^{*s}$, and their tensor products…

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…

In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D(H_n(q))$ of Taft Hopf algebras $H_n(q)$. Tensor product decomposition rules for all finite dimensional…

Let $D$ be a division ring infinite-dimensional over its center $k$ with multiplicative group $D^{\times}$. We show that if $D$ belongs to certain families, there exist free symmetric and unitary pairs in $D^{\times}$ with respect to a…

We show that $\mathcal{U}(\mathbb{Z}G)$, the unit group of the integral group ring $\mathbb{Z} G$, either satisfies Kazhdan's property (T) or is, up to commensurability, a non-trivial amalgamated product, in case $G$ is a finite group…

Recently (hep-th/9307183) we showed that for the case of the WZW- and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral…

Using a recent classification of $\operatorname{End}(\mathcal{D}(G))$, we determine a number of properties for $\operatorname{Aut}(\mathcal{D}(G))$, where $\mathcal{D}(G)$ is the Drinfel'd double of a finite group $G$. Furthermore, we…

Drinfeld showed that any finite dimensional Hopf algebra \G extends to a quasitriangular Hopf algebra \D(\G), the quantum double of \G. Based on the construction of a so--called diagonal crossed product developed by the authors, we…

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep(PSL(2,q)), q prime-power, by applying a Verlinde-like formula on the…

Given a pair of fusion categories $C$ and $D$, we may form the free product $C * D$ and the tensor product $C \boxtimes D$. It is natural to think of the tensor product as a quotient of the free product. What other quotients are possible?…

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…

The purpose of the present paper is to investigate a fusion rule algebra arising from irreducible characters of a compact group $G$ and a closed subgroup $G_0$ of $G$ with finite index. The convolution of this fusion rule algebra is…

Let $A$ be the ring of elements in an algebraic function field $K$ over $\mathbb{F}_q$ which are integral outside a fixed place $\infty$. In contrast to the classical modular group $SL_2(\mathbb{Z})$ and the Bianchi groups, the {\it…

Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is finitely…

A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these…

Let $G$ be a simple algebraic group over an algebraically closed field $\Bbbk$ of positive characteristic. We consider the questions of when the tensor product of two simple $G$-modules is multiplicity free or completely reducible. We…

A remarkable result at the intersection of number theory and group theory states that the order of a finite group $G$ (denoted $|G|$) is divisible by the dimension $d_R$ of any irreducible complex representation of $G$. We show that the…

We study exact sequences of finite tensor categories of the form $\Rep G \to \C \to \D$, where $G$ is a finite group. We show that, under suitable assumptions, there exists a group $\Gamma$ and mutual actions by permutations $\rhd: \Gamma…