标题： 近核维数对于拟阿贝尔群 显示英文标题

标题： Nuclear Dimension for Virtually Abelian Groups

摘要： 设$G$是一个有限生成的拟阿贝尔群。 我们证明了 Hirsch长度，$h(G)$，等于其群 $C^*$-代数的核维数，$\dim_{nuc}(C^*(G))$。 然后我们将注意力专门集中在被称为$\textit{crystal-like}$的晶体群的一个推广上。 我们演示在这种情况下一个$\textit{point group}$是明确定义的，并且这个点群的阶由$C^*$-同构保持。 此外，我们在这种类似晶体的设置中提供了一个关于$C^*$-超刚性的反例。 显示英文摘要

摘要： Let $G$ be a finitely generated virtually abelian group. We show that the Hirsch length, $h(G)$, is equal to the nuclear dimension of its group $C^*$-algebra, $\dim_{nuc}(C^*(G))$. We then specialize our attention to a generalization of crystallographic groups dubbed $\textit{crystal-like}$. We demonstrate that in this scenario a $\textit{point group}$ is well defined and the order of this point group is preserved by $C^*$-isomorphism. In addition, we provide a counter-example to $C^*$-superrigidity within this crystal-like setting.