A note on intermediate subfactors
A note on intermediate subfactors
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DOI：
10.2140/pjm.1994.163.201
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发表时间：
1994-04
影响因子：
0.6
通讯作者：
D. Bisch
中科院分区：
文献类型：
--
作者：
D. Bisch
证明了如果N-C-M-C-P是具有有限Jones指数的II-I因子的包含，使得N-C-P有有限深度，则N-C-M和M-C-P有有限深度.我们通过研究McP和NcP的迭代基本结构来证明这一结果。特别地，我们的证明给出了关于NcM分别的图的详细信息。此外，我们用N‘ΠPI中的Jones投影给出了中间子因子的抽象刻画，其中NcP是NcP的基本结构，并举例说明了如果NcM和McP有有限深度，则NcP不一定有有限深度。
In this note we prove that if N c M c P is an inclusion of II i factors with finite Jones index such that N c P has finite depth, then N C M and M c P have finite depth. We show this result by studying the iterated basic constructions for M c P and N c P. In particular our proof gives detailed information about the graphs for N c M resp. M c P. Furthermore, we give an abstract characterization of intermediate subfactors in terms of Jones projections in N' Π Pi, where N c P C P\ is the basic construction forNcP and give examples showing that if N c M and M c P have finite depth, then N c P does not necessarily have finite depth.