{"paper":{"title":"$\\mathbb{Z}$-graded rings as Cuntz-Pimsner rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Huanhuan Li, James Fletcher, Lisa Orloff Clark, Roozbeh Hazrat","submitted_at":"2018-08-30T04:32:49Z","abstract_excerpt":"Given a $\\mathbb{Z}$-graded ring $A$ and a subring $R\\subseteq A$, it is natural to ask whether $A$ can be realised as the Cuntz-Pimsner ring of some $R$-system. In this paper, we derive sufficient conditions on $A$ and $R$ for this to be the case. As an application, we give conditions under which the Steinberg algebra $A_K(\\mathcal{G})$ associated to a $\\mathbb{Z}$-graded groupoid $\\mathcal{G}=\\sqcup_{n\\in \\mathbb{Z}} \\mathcal{G}_n$ can be realised as the Cuntz-Pimsner ring of an $A_K(\\mathcal{G}_0)$-system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10114","kind":"arxiv","version":2},"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"}