{"paper":{"title":"Quotients of Ultragraph C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hossein Larki","submitted_at":"2015-11-25T18:29:24Z","abstract_excerpt":"Let $\\mathcal{G}$ be an ultragraph and let $C^*(\\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\\mathcal{G})$, we analyze the structure of the quotient $C^*$-algebra $C^*(\\mathcal{G})/I_{(H,B)}$. For simplicity's sake, we first introduce the notion of quotient ultragraph $\\mathcal{G}/(H,B)$ and an associated $C^*$-algebra $C^*(\\mathcal{G}/(H,B))$ such that $C^*(\\mathcal{G}/(H,B))\\cong C^*(\\mathcal{G})/I_{(H,B)}$. We then prove the gauge invariant and the Cuntz-Krieger uniqueness theorems for $C^*(\\mathcal{G}/(H,B))$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00346","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"}