Generalized Longo-Rehren subfactors and alpha-induction

Longo-Rehren subfactors arising from $α$-induction

We study (dual) Longo-Rehren subfactors $M\otimes M^{opp} \subset R$ arising from various systems of endomorphisms of M obtained from alpha-induction for some braided subfactor $N\subset M$. Our analysis provides useful tools to determine the systems of R-R morphisms associated with such Longo-Rehren subfactors, which constitute the ``quantum double'' systems in an appropriate sense. The key to our analysis is that alpha-induction produces half-braidings in the sense of Izumi, so that his general theory can be applied. Nevertheless, alpha-induced systems are in general not braided, and thus ou…

关于 $G$-分级 C$^*$-张量范畴的相对中心构造及 Longo-Rehren 包含关系

Relative center construction for $G$-graded C$^*$-tensor categories and Longo-Rehren inclusions

本文从 Longo-Rehren 包含关系的角度探讨了 $G$-分级 C$^*$-张量范畴的相对中心构造及 $G$-编织结构的存在性。

Orbifold aspects of the Longo-Rehren subfactors

In this article, we will prove that the subsectors of $α$-induced sectors for $M \rtimes \hat{G} \supset M$ forms a modular category, where $M \rtimes \hat{G}$ is the crossed product of $M$ by the group dual $\hat{G}$ of a finite group $G$. In fact, we will prove that it is equivalent to Müger's crossed product. By using this identification, we will exhibit an orbifold aspect of the quantum double of $Δ$(not necessarily non-degenerate) obtained from a Longo-Rehren inclusion $A \supset B_Δ$ under certain assumptions. We will apply the above description of the quantum double of $Δ$ to the Reshet…

等变辫子张量范畴中与α-归纳相关的Frobenius代数

Frobenius algebras associated with the $α$-induction for equivariantly braided tensor categories

本研究在G-辫子多张量范畴中给出G-等变α-归纳的范畴定义，在中性double范畴中构造G-等变α-归纳Frobenius代数，还定义G-等变全中心并证明其与该代数一致，推广了已有相关定理与构造。

Generalized Orbifold Construction for Conformal Nets

Let $\mathcal{B}$ be a conformal net. We give the notion of a proper action of a finite hypergroup acting by vacuum preserving unital completely positive (so-called stochastic) maps, which generalizes the proper actions of finite groups. Taking fixed points under such an action gives a finite index subnet $\mathcal{B}^K$ of $\mathcal{B}$, which generalizes the $G$-orbifold. Conversely, we show that if $\mathcal{A}\subset \mathcal{B}$ is a finite inclusion of conformal nets, then $\mathcal{A}$ is a generalized orbifold $\mathcal{A}=\mathcal{B}^K$ of the conformal net $\mathcal{B}$ by a unique f…