论文标题
没有财产伽玛
An exotic II$_1$ factor without property Gamma
论文作者
论文摘要
我们引入了一种新的迭代合并的免费产品II $ _1 $因子的免费产品，并使用它来构建一个可分离的II $ _1 $因子，该因子没有财产伽玛，并且并不等同于自由组因子$ \ text {l text {l}（\ mathbb f_n）$，对于任何$ 2 \ leq n \ leq n \ leq n \ leq les \ leq \ fe unf。这提供了两个没有属性伽玛的两个非元素等效II $ _1 $因素的明确示例。此外，我们的施工还提供了一个没有属性伽玛的II $ _1 $因子的第一个明确示例，这也不是基本等于矩阵代数的任何超强。我们的证明使用Voiculescu的自由熵理论和Popa的变形/刚性理论的技术融合。
We introduce a new iterative amalgamated free product construction of II$_1$ factors, and use it to construct a separable II$_1$ factor which does not have property Gamma and is not elementarily equivalent to the free group factor $\text{L}(\mathbb F_n)$, for any $2\leq n\leq \infty$. This provides the first explicit example of two non-elementarily equivalent II$_1$ factors without property Gamma. Moreover, our construction also provides the first explicit example of a II$_1$ factor without property Gamma that is also not elementarily equivalent to any ultraproduct of matrix algebras. Our proofs use a blend of techniques from Voiculescu's free entropy theory and Popa's deformation/rigidity theory.
