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Houdayer, Cyril; Isono, Yusuke
Advances in mathematics (New York. 1965), 01/2017, Volume: 305Journal Article
We show that whenever m≥1 and M1,…,Mm 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 M1⊗‾⋯⊗‾Mm retains the integer m and each factor Mi 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 M1,…,Mm 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 III1 factors in the class C(AO).
