A characterization of a finite-dimensional commuting square producing a subfactor of finite depth
A characterization of a finite-dimensional commuting square producing a subfactor of finite depth
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产生有限深度子因子的有限维通勤广场的表征
DOI：
10.1093/imrn/rnac082
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Y. Kawahigashi
中科院分区：
文献类型：
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作者：
Y. Kawahigashi
我们给出了一个有限维交换平方的-代数的正规化迹，产生一个超有限的II型子因子的有限指数和有限深度的Morita等价酉融合范畴的一个特征。这种类型的交换广场研究了N。佐藤和我们表明，他的建设略有推广，涵盖了充分的一般情况下，这种通勤广场。我们还给出了这样一个交换平方，产生一个给定的超有限型II子因子的有限指数和有限深度的一个特征。这些结果也给出了某些4-张量，出现在最近的研究中的矩阵乘积算子在二维拓扑秩序的一个特征。
We give a characterization of a finite-dimensional commuting square of-algebras with a normalized trace that produces a hyperfinite type IIsubfactor of finite index and finite depth in terms of Morita equivalent unitary fusion categories. This type of commuting squares was studied by N. Sato and we show that a slight generalization of his construction covers the fully general case of such commuting squares. We also give a characterization of such a commuting square that produces a given hyperfinite type IIsubfactor of finite index and finite depth. These results also give a characterization of certain 4-tensors that appear in recent studies of matrix product operators in 2D topological order.