论文标题
扩散痕迹和HAAR单位
Diffuse traces and Haar unitaries
论文作者
论文摘要
我们表明，在且仅当它是扩散时，仅当且仅当它不主导通过有限维二维商来占据因素的奇特功能时，就可以在且仅当它弥漫时承认一个统一的奇特状态。因此，当且仅当其每个奇特国家都承认HAAR统一时，一个Unital c*-Algebra没有有限维的表示。 更普遍地，我们研究非地国家何时接纳HAAR单位。特别是，我们表明，在Unital，简单，无限的C*-Algebra上的每个州都承认了Haar Unity。 我们为减少的自由产品的结构提供了应用。值得注意的是，简单的C*-ergebras的奇特还原自由产品始终是稳定等级的简单C*-代数。
We show that a tracial state on a unital C*-algebra admits a Haar unitary if and only if it is diffuse, if and only if it does not dominate a tracial functional that factors through a finite-dimensional quotient. It follows that a unital C*-algebra has no finite-dimensional representations if and only if each of its tracial states admits a Haar unitary. More generally, we study when nontracial states admit Haar unitaries. In particular, we show that every state on a unital, simple, infinite-dimensional C*-algebra admits a Haar unitary. We obtain applications to the structure of reduced free products. Notably, the tracial reduced free product of simple C*-algebras is always a simple C*-algebra of stable rank one.
