{"paper":{"title":"Groupoid algebras as covariance algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"James Fletcher, Lisa Orloff Clark","submitted_at":"2019-06-07T01:32:38Z","abstract_excerpt":"Suppose $\\mathcal{G}$ is a second-countable locally compact Hausdorff \\'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\\mathcal{G}\\rightarrow G$ is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid $C^*$-algebra $C_r^*(\\mathcal{G})$ may be realised naturally as the covariance algebra of a product system over $P$ with coefficient algebra $C_r^*(c^{-1}(e))$. When $(G,P)$ is a quasi-lattice ordered group, we also derive conditions that allow $C_r^*(\\mathcal{G})$ to be realised as the Cuntz--Nica--Pimsner algebra of a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02855","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":""},"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"}