A disintegration theorem for non-second-countable etale groupoids
arXiv:2607.06010
The paper provides a self‑contained proof of a disintegration theorem for C*-algebras of possibly non‑Hausdorff étale groupoids that can be covered by countably many open bisections, and explores related constructions such as the I‑norm, inverse semigroup crossed products, and KMS states.
Abstract
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 -norm, crossed product decompositions by inverse semigroup actions, and KMS-states and weights for general étale groupoid C-algebras.
27 pages; v3: minor changes; v2: a section on inverse semigroup crossed products and a discussion of the Steinberg algebras added, more references, minor fixes