论文标题
W $^*$和C $^*$的新示例 - 超级群组
New examples of W$^*$ and C$^*$-superrigid groups
论文作者
论文摘要
如果从其von Neumann algebra $ l（g）$完全识别它，则$ g $称为$ w^*$ - superrigid（resp。$ c^*$ - superrigid），如果它完全可以识别。在POPA的变形/刚性理论中开发新的技术方面，我们介绍了几个新类别的$ W^*$ - 超级群体，它们以直接产品，具有不可弥补的核心的半领产品以及合并的免费产品和HNN-Extensions的迭代。作为副产品，我们获得了新的刚性导致$ c^*$ - 代数理论，其中包括$ c^*$ - 超级群组的其他示例，以及对减少组$ c^*$代数的对称的明确计算。
A group $G$ is called $W^*$-superrigid (resp. $C^*$-superrigid) if it is completely recognizable from its von Neumann algebra $L(G)$ (resp. reduced $C^*$-algebra $C_r^*(G)$). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several new classes of $W^*$-superrigid groups which appear as direct products, semidirect products with non-amenable core and iterations of amalgamated free products and HNN-extensions. As a byproduct we obtain new rigidity results in $C^*$-algebra theory including additional examples of $C^*$-superrigid groups and explicit computations of symmetries of reduced group $C^*$-algebras.
