The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory
The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory
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DOI：
10.1007/s002200000234
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发表时间：
2000-09
影响因子：
2.4
通讯作者：
Masaki Izumi
中科院分区：
文献类型：
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作者：
Masaki Izumi
本文研究了因子自同态有限闭系统的Longo-Ehren包含的结构，其范畴结构与A.奥克内亚努特别是，我们得到了一个精确的描述与Longo-Escherren夹杂物的半编织，这不一定满足通常的条件编织的部门。在这样做的时候，我们给新的证明，大多数已知的陈述有关的渐近包含。我们利用半辫构造了管代数的一个完整的矩阵单位系统，第二部分将用它来描述Cuntz代数自同态所产生的Longo-Escherren包含的具体例子.我们还讨论了原系统有辫子的情况，推广了Ocneanu和Evans-Kawahigashi分析Hecke代数子因子的渐近包含的方法。
We investigate the structure of the Longo–Rehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the Longo–Rehren inclusions in terms of half braidings, which do not necessarily satisfy the usual condition of braidings. In doing so, we give new proofs to most of the known statements concerning asymptotic inclusions. We construct a complete system of matrix units of the tube algebra using the half braidings, which will be used in the second part to describe concrete examples of the Longo–Rehren inclusions arising from the Cuntz algebra endomorphisms. We also discuss the case where the original system has a braiding, and generalize Ocneanu and Evans–Kawahigashi's method for the analysis of the asymptotic inclusions of the Hecke algebra subfactors.