Q-system completion for C⁎ 2-categories

  title={Q-system completion for C⁎ 2-categories},
  author={Quanlin Chen and Roberto Hern{\'a}ndez Palomares and Corey Jones and David Penneys},
  journal={Journal of Functional Analysis},

Q-system completion is a 3-functor

Q-systems are unitary versions of Frobenius algebra objects which appeared in the theory of subfactors. In recent joint work with R. Hernández Palomares and C. Jones, the authors defined a notion of

K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C∗-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on

On a Connes Fusion Approach to Finite Index Extensions of Conformal Nets

In the framework of Connes fusion, we discuss the relationship between the (non-necessarily local or irreducible) finite index extensions B of an irreducible local Möbius covariant net A and the C

Haploid algebras in $C^*$-tensor categories and the Schellekens list

. We prove that a haploid associative algebra in a C ∗ -tensor category C is equivalent to a Q-system (a special C ∗ -Frobenius algebra) in C if and only if it is rigid. This allows us to prove the

Unitary connections on Bratteli diagrams

. In this paper, we extend Ocneanu’s theory of connections on graphs to define a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are generalizations of unitary connections.

Unitary braided-enriched monoidal categories

. Braided-enriched monoidal categories were introduced in work of Morrison-Penneys, where they were characterized using braided central functors. Recent work of Kong-Yuan-Zhang-Zheng and Dell

A planar algebraic description of conditional expectations

Let N ⊂ M be a unital inclusion of arbitrary von Neumann algebras. We give a 2- C ∗ -categorical/planar algebraic description of normal faithful conditional expectations E : M → N ⊂ M with finite

A categorical Connes' $\chi(M)$

Popa introduced the tensor category χ̃(M) of approximately inner, centrally trivial bimodules of a II1 factor M , generalizing Connes’ χ(M). We extend Popa’s notions to define the W-tensor category

A covariant Stinespring theorem

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let [Formula: see text] be the rigid C*-tensor category of

Unitary anchored planar algebras

In our previous article [arXiv:1607.06041], we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of



Q-system completion is a 3-functor

Q-systems are unitary versions of Frobenius algebra objects which appeared in the theory of subfactors. In recent joint work with R. Hernández Palomares and C. Jones, the authors defined a notion of

Q-systems and compact W*-algebra objects

We show that given a rigid C*-tensor category, there is an equivalence of categories between normalized irreducible Q-systems, also known as connected unitary Frobenius algebra objects, and compact

Quasitraces on exact C*-algebras are traces

It is shown that all 2-quasitraces on a unital exact C-algebra are traces. As consequences one gets: (1) Every stably finite exact unital Calgebra has a tracial state, and (2) if an AW -factor of

Realizations of rigid C*-tensor categories as bimodules over GJS C*-algebras

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

Crossed products of continuous-trace *-algebras by smooth actions

We study in detail the structure of C*-crossed products of the form A> G, where A is a continuous-trace algebra and a is an action of a locally compact abelian group G on A, especially in the case

Anomalous symmetries of classifiable C*-algebras

We study the H invariant of a group homomorphism φ : G → Out(A), where A is a classifiable C∗-algebra. We show the existence of an obstruction to possible H invariants arising from considering the

Categorically Morita equivalent compact quantum groups

We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting

An Equivariant Brauer Group and Actions of Groups onC*-Algebras

Suppose that (G, T) is a second countable locally compact trans- formation group given by a homomorphism l : G → Homeo(T), and that A is a separable continuous-trace C ∗ -algebra with spectrum T. An

Frobenius Structures Over Hilbert C*-Modules

We study the monoidal dagger category of Hilbert C*-modules over a commutative C*-algebra from the perspective of categorical quantum mechanics. The dual objects are the finitely presented projective

Inner Product Modules Over B ∗ -Algebras

This paper is an investigation of right modules over a B*algebra B which posses a B-valued "inner product" respecting the module action. Elementary properties of these objects, including their