We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof, by using the author’s Disintegration Theorem for groupoid representations. We also prove that every primitive ideal is the kernel of an induced representation from an isotropy group; however, we are unable to show, in general, that it is the kernel of an irreducible induced representation. If each isotropy group is finite (e.g., if the groupoid is principal) and if the base ring is Artinian (e.g., a field), then we can show that every primitive ideal is the kernel of an irreducible representation induced from isotropy.

中文翻译：

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étale groupoid 代数的理想和 Exel 的 Effros-Hahn 猜想

我们将 Demeneghi 最近的一个结果扩展到任意交换基环，即一个域上的充足群状代数的每个理想都是来自各向同性群的诱导表示的核的交集，通过使用作者的分解定理进行群状表示，证明要短得多. 我们还证明了每个原始理想都是各向同性群的诱导表示的核；然而，一般来说，我们无法证明它是不可约诱导表示的内核。如果每个各向同性群都是有限的（例如，如果群状体是主体），并且基环是亚丁环（例如，场），那么我们可以证明每个原始理想都是由各向同性导出的不可约表示的核。