论文标题
左取消单肌的非Hausdorff etale gropoids和C* - 代数
Non-Hausdorff etale groupoids and C*-algebras of left cancellative monoids
论文作者
论文摘要
我们研究了一个问题，是否由局部紧凑的Étalegroupoid的单位空间的密集子集定义的表示形式足以确定群体c $^*$ - 代数的降低规范。我们提出了足够的条件以进行任一结论，当各向同性组无扭转时，给出了完整的答案。作为一个应用，我们考虑spielberg与左取消的单型$ s $相关的groupoid $ g（s）$，并为规范地图$ c $ c^*_ r（g（s）\ c^*_ r（s）\ c^*_ r（s）$，我们称之为c $^*$ - 规律性c $^*$ - 代数$ c^*（s）= c^*（g（s））$。我们给出了两个相关示例的左取消型单体$ s $和$ t $，这样两者都不有限地对准并且具有非Hausdorff相关的étalegropsoids，但是$ s $是c $^*$ - 常规，而$ t $却不是。
We study the question whether the representations defined by a dense subset of the unit space of a locally compact étale groupoid are enough to determine the reduced norm on the groupoid C$^*$-algebra. We present sufficient conditions for either conclusion, giving a complete answer when the isotropy groups are torsion-free. As an application we consider the groupoid $G(S)$ associated to a left cancellative monoid $S$ by Spielberg and formulate a sufficient condition, which we call C$^*$-regularity, for the canonical map $C^*_r(G(S))\to C^*_r(S)$ to be an isomorphism, in which case $S$ has a well-defined full semigroup C$^*$-algebra $C^*(S)=C^*(G(S))$. We give two related examples of left cancellative monoids $S$ and $T$ such that both are not finitely aligned and have non-Hausdorff associated étale groupoids, but $S$ is C$^*$-regular, while $T$ is not.
