A unique decomposition result for HT factors with torsion free core

We prove that II1factors have a unique (up to unitary conjugacy) cross-product type decomposition around “core subfactors” satisfying the property HT of [S. Popa, On a class of type II1factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809–899] and a certain “torsion freeness” condition. In particular, this shows that isomorphism of factors of the form , , for free groups of rank and , , implies .

我们证明了II₁型因子在满足[S. Popa，《关于一类具有贝蒂数不变量的II₁型因子》，《数学年刊》（2）163（2006）809 - 899]中的性质HT以及某个“无挠性”条件的“核心子因子”周围具有唯一的（在酉共轭意义下）交叉积型分解。特别地，这表明对于秩为 的自由群 和 ，形如 ， 的因子同构意味着 。