论文标题
关于étalegropoids C* - 代数的理想结构的一些结果
Some results regarding the ideal structure of C*-algebras of étale groupoids
论文作者
论文摘要
我们证明了内部固有局部紧凑的Hausdorffétalegroupoids的夹心引理。我们的引理说，这种类别素的$ c^*$ - 代数的每个理想都夹在与单位空间的两个独特定义的开放不变子集相关的理想之间。我们获得了减少的$ c^*$ - 代数的理想和由两个嵌套开放式不变套件组成的三元组，并且在$ c^*$ - 代数的$ c^*$ - 代数中，他们确定它们与对角度亚代艾尔格拉和全方位支撑具有琐碎的相交。然后，我们对ARA和LOLK的群体固定介绍了部分动作的相对强拓扑条件，并证明减少了$ C^*$ - 内部实行局部紧凑型Hausdorffétalegropsoids的代数，满足了这种情况，可以在Ara和Lolk的含义中理想。
We prove a sandwiching lemma for inner-exact locally compact Hausdorff étale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined open invariant subsets of the unit space. We obtain a bijection between ideals of the reduced $C^*$-algebra, and triples consisting of two nested open invariant sets and an ideal in the $C^*$-algebra of the subquotient they determine that has trivial intersection with the diagonal subalgebra and full support. We then introduce a generalisation to groupoids of Ara and Lolk's relative strong topological freeness condition for partial actions, and prove that the reduced $C^*$-algebras of inner-exact locally compact Hausdorff étale groupoids satisfying this condition admit an obstruction ideal in Ara and Lolk's sense.
