Longo-Rehren subfactors arising from a-induction
Longo-Rehren subfactors arising from a-induction
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由 a 归纳产生的 Longo-Rehren 子因子
DOI：
10.2977/prims/1145476688
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发表时间：
2001
影响因子：
1.2
通讯作者：
Yasuyuki Kawahigashi
中科院分区：
文献类型：
--
作者：
Jens Böckenhauer;David E. Evans;Yasuyuki Kawahigashi
本文研究了M的各种自同态系统所产生的（对偶）Longo-Mogren子因子M <$Mopp <$Mogren，这些自同态系统是由M的某些辫子子因子N <$M的α-归纳得到的.我们的分析提供了有用的工具，以确定系统的？？我们分析的关键是α-归纳产生Izumi意义下的半辫，因此可以应用他的一般理论。然而，α诱导的系统通常不是编织的，因此我们的结果允许计算（某些）系统的量子双没有编织。我们通过几个例子来说明我们的一般结果，包括计算量子双系统的E8子因子的渐近包含以及它的三个类似物所产生的SU（3）k的共形包含。
We study (dual) Longo–Rehren subfactors M ⊗ Mopp ⊂ ℝ arising from various systems of endomorphisms of M obtained from α-induction for some braided subfactor N ⊂ 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 α-induction produces half-braidings in the sense of Izumi, so that his general theory can be applied. Nevertheless, α-induced systems are in general not braided, and thus our results allow to compute the quantum doubles of (certain) systems without braiding. We illustrate our general results by several examples, including the computation of the quantum double systems for the asymptotic inclusion of the E8 subfactor as well as its three analogues arising from conformal inclusions of SU(3)k.