{"paper":{"title":"Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Relative Cuntz-Pimsner algebras arising from groupoid correspondences are themselves groupoid C*-algebras.","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ralf Meyer","submitted_at":"2025-06-24T12:30:49Z","abstract_excerpt":"A groupoid correspondence on an etale, locally compact groupoid induces a C*-correspondence on its groupoid C*-algebra. We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid. We describe this groupoid explicitly and characterise it by a universal property that specifies its actions on topological spaces. Our construction unifies the construction of groupoids underlying the C*-algebras of topological graphs and self-similar groups."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input is an etale locally compact groupoid equipped with a groupoid correspondence whose induced C*-correspondence admits a relative Cuntz-Pimsner construction with respect to the ideal coming from an open invariant subset.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Relative Cuntz-Pimsner algebras arising from groupoid correspondences are themselves groupoid C*-algebras.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"eec32799abf0734d57c2dc2bf844d55367ffd78914b5831a92fe9dbde82e506a"},"source":{"id":"2506.19569","kind":"arxiv","version":3},"verdict":{"id":"cece7208-12c2-4cfe-a825-1f328d020e5a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T08:08:22.887628Z","strongest_claim":"We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid.","one_line_summary":"The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input is an etale locally compact groupoid equipped with a groupoid correspondence whose induced C*-correspondence admits a relative Cuntz-Pimsner construction with respect to the ideal coming from an open invariant subset.","pith_extraction_headline":"Relative Cuntz-Pimsner algebras arising from groupoid correspondences are themselves groupoid C*-algebras."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.19569/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":25,"sample":[{"doi":"","year":2015,"title":"Thesis, Georg-August- Universität Göttingen, 2015, http://hdl.handle.net/11858/00-1735-0000-0028-87E8-C","work_id":"2c692ae0-fdbb-4e26-b552-6f99075d1bfa","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.53846/goediss-10930","year":2024,"title":"Thesis, Georg-August-Universität Göttingen, 2024","work_id":"a74c7aba-636b-427a-bcfa-b9cd9045ec5a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Math.28 (2022), 1329–1364, available athttps://nyjm.albany.edu/j/2022/28-56","work_id":"301aa87c-2a7f-4a74-81ea-2e7c27331600","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1112/plms.12131.mr3851326","year":2018,"title":"Alcides Buss, Rohit Holkar, and Ralf Meyer,A universal property for groupoid C∗-algebras. I, Proc. Lond. Math. Soc. (3)117 (2018), no. 2, 345–375, doi: 10.1112/plms.12131.MR3851326 34 RALF MEYER","work_id":"61307607-76a9-45f6-9d7d-3ff4ca840c32","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1216/rmj-2017-47-1-53","year":2017,"title":"Alcides Buss and Ralf Meyer,Inverse semigroup actions on groupoids, Rocky Mountain J. Math. 47 (2017), no. 1, 53–159, doi: 10.1216/RMJ-2017-47-1-53. MR3619758","work_id":"8f87052e-b33e-4e61-81fc-0fc6ec2208f2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"331d46b48725cd9fa878596221229fc9da0170b3691b886a0c23e4777aa54eee","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"}