Unique prime factorization and bicentralizer problem for a class of type III factors
Unique prime factorization and bicentralizer problem for a class of type III factors
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DOI：
10.1016/j.aim.2016.09.030
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
Cyril Houdayer;Yusuke Isono
中科院分区：
文献类型：
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作者：
Cyril Houdayer;Yusuke Isono
我们证明了，当m≥ 1且M1，.，Mm是一个包含所有自由Araki-Woods因子的大类von Neumann代数C（AO）中的不可修正因子时，张量积因子M1 Mm在置换指数后保持整数m和每个因子Mi直到稳定同构.我们的方法统一了[33]，[25]中的唯一素因子分解（UPF）结果，并且在M1，...，Mm是自由Araki-Woods因子的情况下提供了新的UPF结果。为了获得上述UPF结果，我们证明了Connes的双中心化问题有一个正解的所有类型I I I 1的因素在类C（AO）。
We show that whenever m≥ 1 and M 1,…, M m are nonamenable factors in a large class of von Neumann algebras that we call C (AO) and which contains all free Araki–Woods factors, the tensor product factor M 1⊗‾⋯⊗‾ M m retains the integer m and each factor M i up to stable isomorphism, after permutation of the indices. Our approach unifies the Unique Prime Factorization (UPF) results from [33],[25] and moreover provides new UPF results in the case when M 1,…, M m are free Araki–Woods factors. In order to obtain the aforementioned UPF results, we show that Connes's bicentralizer problem has a positive solution for all type I I I 1 factors in the class C (AO).