可测性刻画的弗鲁斯滕伯格×p,×q猜想
A tracial characterization of Furstenberg's $\times p,\times q$ conjecture
AI总结：
本文研究了交换群的几乎极小作用及其交叉积，证明了当p和q乘积无关时，弗鲁斯滕伯格×p,×q猜想成立当且仅当群Z[1/pq]⋊Z²的C*代数上仅有一个忠实极值迹。
摘要：
我们研究了交换群的几乎极小作用及其交叉积。作为应用，给定乘积无关的整数p和q，我们证明弗鲁斯滕伯格的×p,×q猜想成立当且仅当群Z[1/pq]⋊Z²的C*代数上仅有一个忠实极值迹。我们还计算了该C*代数的原始理想空间和K-理论。
英文摘要：
We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers $p$ and $q$, we show that Furstenberg's $\times p,\times q$ conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the $C^*$-algebra of the group $\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2$. We also compute the primitive ideal space and K-theory of $C^*(\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
