关于Kumjian的C ~*-对角线与不透明理想
On Kumjian's C*-diagonals and the opaque ideal
摘要：
我们刻画了扭曲的主Etale群胚的奇异C* 代数，以及单位空间的交换子代数，作为C* 代数的包含体“$A\subseteq B$“，其中$A$是交换的，正则的，并满足扩张性质（纯态唯一地扩张到$B$）。当$B$是核理想时，我们推出相应的不透明理想是平凡的。作为应用，我们给出了Kumjian的C*-对角代数是满足扩张性质的正则交换子代数的一个简化的刻画，其不透明理想为零。
英文摘要：
We characterize exotic C*-algebras of twisted, principal étale groupoids, together with the abelian subalgebra associated to the unit space, as precisely being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian, regular, and satisfies the extension property (pure states extend uniquely to $B$). When $B$ is moreover nuclear, we deduce that the corresponding opaque ideal is trivial. As an application, we give a streamlined characterization of Kumjian's C*-diagonals as the regular abelian subalgebras satisfying the extension property with vanishing opaque ideal.
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