Related papers: $II_1$-Subfactors associated with the $C^*$-Tensor…

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided…

For any finite dimensional C*-algebra A with any trace vector {\vec s} whose components are rational numbers, we give an endomorphism {\Phi} of the hyperfinite II_1 factor R such that: forall k in {\mathbb N} {\Phi}^k (R)' \cap R= \otimes^k…

Given an arbitrary countably generated rigid C*-tensor category, we construct a fully-faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital…

We show that the rigid C*-tensor categories of finite dimensional type 1 unitary representations of the quantum groups $U_{q}(\mathfrak{g}_{2})$ corresponding to the exceptional Lie group $G_2$ for positive $q\ne 1$ have property (T).

We establish a correspondence between the levels of Verlinde rings and the depths of subfactors. Given the $l$-level Verlinde ring $R_l(G)$ of a simple compact Lie group $G$, the tensor products of fundamental representations give us the…

In this paper, we generalize Izumi's result on uniqueness of realization of finite C$^*$-tensor categories in the endomorphism category of the injective factor of type II_1 for finitely generated strongly amenable C$^*$-tensor categories by…

We associate to each Temperley-Lieb-Jones C*-tensor category $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ with parameter $\delta$ in the discrete range $\{2\cos(\pi/(k+2))\,:\,k=1,2,\ldots\}\cup\{2\}$ a certain C*-algebra $\mathcal{B}$ of…

We study tensor structures on (Rep G)-module categories defined by actions of a compact quantum group G on unital C*-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of…

We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of…

For a braided tensor category C and a subcategory K there is a notion of centralizer C_C(K), which is a full tensor subcategory of C. A pre-modular tensor category is known to be modular in the sense of Turaev iff the center Z_2(C):=C_C(C)…

We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra $A$ generated by an irreducible representation of such a group has…

In our article [arXiv:1511.05226], we studied the commutant $\mathcal{C}'\subset \operatorname{Bim}(R)$ of a unitary fusion category $\mathcal{C}$, where $R$ is a hyperfinite factor of type $\rm II_1$, $\rm II_\infty$, or $\rm III_1$, and…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…

A finite pre-tensor category is a finite abelian category equipped with a right exact tensor product for which every projective object has duals. Finite tensor categories, for which every object has duals, are notable examples. More…

Let $M$ be a $\rm II_1$ factor and let $\mathcal{F}(M)$ denote the fundamental group of $M$. In this article, we study the following property of $M$: for arbitrary $\rm II_1$ factor $B$, we have $\mathcal{F}(M \overline{\otimes}…

In this paper we examine bases for finite index inclusion of $II_1$ factors and connected inclusion of finite dimensional $C^*$- algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied…

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors ?^{**} and D tensor ^{**}? tensor D^{-1}. This…

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a…