Related papers: Categorical duality for Yetter-Drinfeld algebras

We give criteria for when finitely generated local modules over a commutative algebra $A$ in the ind-completion $\widehat{\mathcal{C}}$ of a braided tensor category $\mathcal{C}$ inherit the structure of a (rigid, braided, ribbon) tensor…

We provide a reference for basic categorial properties of the categories of (possibly non-unital) $\mathbb{C}$-linear $*$-categories or $C^{*}$-categories, and (not necessarily unit-preserving) functors. Generalizing the classical case of…

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences…

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{i\pi/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor…

In the present work, we study Yetter-Drinfeld algebras over a pairing of multiplier Hopf algebras. Our main motivation is the construction of a self-dual theory of (C*-)algebraic quantum transformation groupoids. Instead of the standard…

Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the…

We construct several new classes of bifunctors $(A,B)\mapsto A\otimes_{\alpha} B$, where $A\otimes_\alpha B$ is a cross norm completion of $A\odot B$ for each pair of C*-algebras $A$ and $B$. For the first class of bifunctors considered…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

We consider an interesting class of braidings defined by a combinatorial property in an earlier paper. We show that it consists exactly of those braidings that come from certain Yetter-Drinfeld module structures over pointed Hopf algebras…

We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…

We prove that any non-symmetric ribbon tensor category $\mathcal{C}$ with the fusion rules of the compact group of type $G_2$ needs to be equivalent to the representation category of the corresponding Drinfeld-Jimbo quantum group for $q$…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…

Given a tensor category C, one constructs its Drinfeld center Z(C) which is a braided tensor category, having as objects pairs (X, lambda), where X in Obj(C) and lambda is a half-braiding. For a premodular category C, we construct a new…

We classify finite pointed braided tensor categories admitting a fiber functor in terms of bilinear forms on symmetric Yetter-Drinfeld modules over abelian groups. We describe the groupoid formed by braided equivalences of such categories…

We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between…

We continue our study of the monoidal category $D(G)$. At the level of cohomology we transfer the duality functor to the derived category of Hecke dg-modules. In the process we develop a more general and streamlined approach to the…

We develop a method for generating the complete set of basic data under the torsorial actions of $H^2_{[\rho]}(G,\mathcal{A})$ and $H^3(G,\text{U}(1))$ on a $G$-crossed braided tensor category $\mathcal{C}_G^\times$, where $\mathcal{A}$ is…