Tensor C*-categories arising as bimodule categories of II_1 factors
Tensor C*-categories arising as bimodule categories of II_1 factors
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张量 C* 类别作为 II_1 因子的双模类别出现
DOI：
10.1016/j.aim.2012.12.020
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Sven Raum
中科院分区：
文献类型：
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作者：
S'ebastien Falguieres;Sven Raum
证明了如果C是某一类中的张量C∗-范畴，则存在一个不可数的两两非稳定同构的II1因子(Mi)族，使得Mi的双模范畴与C等价，特别地，我们证明了每个有限张量C∗-范畴都是II1因子的双模范畴.作为应用，证明了有限指数不可约子因子的指数集为{1，5+132，12+313，4+13，11+3132，13+3132，19+5132，7+132}.的II1因子的存在性我们还给出了II1因子M的第一个例子，使得Bimod(M)是显式计算的，并且具有不可数个不可约对象的同构类。
We prove that if C is a tensor C∗-category in a certain class, then there exists an uncountable family of pairwise non stably isomorphic II1factors (Mi) such that the bimodule category of Miis equivalent to C for all i. In particular, we prove that every finite tensor C∗-category is the bimodule category of a II1factor. As an application we prove the existence of a II1factor for which the set of indices of finite index irreducible subfactors is {1,5+132,12+313,4+13,11+3132,13+3132,19+5132,7+132}. We also give the first example of a II1factor M such that Bimod(M) is explicitly calculated and has an uncountable number of isomorphism classes of irreducible objects.