{"paper":{"title":"The ideal structure of C*-algebras of etale groupoids with isotropy groups of local polynomial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.OA","authors_text":"Johannes Christensen, Sergey Neshveyev","submitted_at":"2024-12-16T14:15:52Z","abstract_excerpt":"Given an amenable second countable Hausdorff locally compact \\'etale groupoid $\\mathcal G$ such that each isotropy group $\\mathcal G^x_x$ has local polynomial growth, we give a description of $\\operatorname{Prim} C^*(\\mathcal G)$ as a topological space in terms of the topology on $\\mathcal G$ and representation theory of the isotropy groups and their subgroups. The description simplifies when either the isotropy groups are FC-hypercentral or $\\mathcal G$ is the transformation groupoid $\\Gamma\\ltimes X$ defined by an action $\\Gamma\\curvearrowright X$ with locally finite stabilizers. To illustra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11805","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}