{"paper":{"title":"Inclusions of Fell bundles $\\mathrm{C}^*$-algebras and coaction crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Md Amir Hossain","submitted_at":"2026-06-11T17:29:27Z","abstract_excerpt":"Let $p \\colon \\mathcal{A} \\to G$ be a Fell bundle over a locally compact Hausdorff second countable groupoid $G$ equipped with a Haar system, and let $\\Gamma$ be a discrete group. Given a continuous $1$-cocycle $c \\colon G \\to \\Gamma$, we show that the $\\mathrm{C}^*$-algebra of the restricted Fell bundle $\\mathcal{A}|_{G_e}$ embeds isometrically into $\\mathrm{C}^*(G;\\mathcal{A})$, where $G_e = c^{-1}(e)$ is the clopen subgroupoid corresponding to the identity element.\n  We exploit this embedding to show that $\\mathrm{C}^*(G;\\mathcal{A})$ admits a natural structure of a topologically graded $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13616","kind":"arxiv","version":1},"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/2606.13616/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"}