具有无挠的核的HT因子的唯一分解结果
A Unique Decomposition Result for HT Factors with Torsion Free Core
摘要：
我们证明了II $_1$因子$M$有一个唯一的（直到酉共轭）围绕"核心子因子“$N \subset M$满足性质HT和一定的”扭自由“条件的交叉积型分解。特别地，这表明，对于无挠的、不顺从子群$Γ\subset SL(2, \Bbb Z)$和$α= e^{2πi t}$，$t \not\in \Bbb Q$，形式为$L_α(\Bbb Z^2) \rtimes Γ$的因子的同构意味着相应群$Γ$的同构。
英文摘要：
We prove that II$_1$ factors $M$ have a unique (up to unitary conjugacy) cross-product type decomposition around ``core subfactors'' $N \subset M$ satisfying the property HT and a certain ``torsion freeness'' condition. In particular, this shows that isomorphism of factors of the form $L_α(\Bbb Z^2) \rtimes Γ$, for torsion free, non-amenable subgroups $Γ\subset SL(2, \Bbb Z)$ and $α= e^{2πi t}$, $t \not\in \Bbb Q$, implies isomorphism of the corresponding groups $Γ$.
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