AI 中文总结
研究非第二可数étale群胚的C* - 代数，给出雷诺分解定理自包含版本，可覆盖可数开双截面，还应用于讨论I - 范数、KMS态和权重等。
AI 中文摘要
我们给出了雷诺分解定理的一个自包含版本，适用于（扭曲的）C* - 代数，该代数来自不一定是豪斯多夫的étale群胚，且可由可数多个开双截面覆盖。作为应用，我们讨论了一般étale群胚C* - 代数上的I - 范数、KMS态和权重。
英文摘要
We give a self-contained account of a version of Renault's disintegration theorem for (twisted) C$^*$-algebras of not necessarily Hausdorff étale groupoids that can be covered by countably many open bisections. As an application we discuss the $I$-norm, crossed product decompositions by inverse semigroup actions, and KMS-states and weights for general étale groupoid C$^*$-algebras.
Comments27 pages; v3: minor changes; v2: a section on inverse semigroup crossed products and a discussion of the Steinberg algebras added, more references, minor fixes
