Generalized Longo–Rehren Subfactors and α-Induction
Generalized Longo–Rehren Subfactors and α-Induction
复制标题
广义 Longo–Rehren 子因子和 α-归纳
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Yasuyuki Kawahigashi
中科院分区：
文献类型：
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作者：
Yasuyuki Kawahigashi
翻译后摘要：我们研究最近建设的子因子，概括了Longo-Escherren的子因子。我们证明了如果我们将这个构造应用于非退化辫状子因子N <$M和α±-归纳，则所得到的子因子与Longo-Escherren子因子M <$Mopp <$R是对偶的，该子因子M <$Mopp R产生于由αplusmn;-归纳产生的M的不可约自同态的整个系统。作为推论，我们否定地解决了Buberren提出的一个辫子存在性问题。此外，我们将我们以前与Longo和Müger关于由S1上的完全有理共形因子网产生的多区间子因子的研究推广到子因子网，并表明（广义）Longo-Ehren子因子和α-归纳自然地出现在这种情况下。
Abstract: We study the recent construction of subfactors by Rehren which generalizes the Longo–Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided subfactor N⊂M and α±-induction, then the resulting subfactor is dual to the Longo–Rehren subfactor M⊗Mopp⊂R arising from the entire system of irreducible endomorphisms of M resulting from αplusmn;-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize our previous study with Longo and Müger on multi-interval subfactors arising from a completely rational conformal net of factors on S1 to a net of subfactors and show that the (generalized) Longo–Rehren subfactors and α-induction naturally appear in this context.