{"paper":{"title":"Reciprocal Cuntz--Krieger algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kengo Matsumoto, Taro Sogabe","submitted_at":"2025-02-25T11:48:46Z","abstract_excerpt":"Reciprocality in Kirchberg algebras is a duality between strong extension groups and K-theory groups. We describe a construction of the reciprocal dual algebra $\\widehat{\\mathcal{A}}$ for a Kirchberg algebra $\\mathcal{A}$ with finitely generated K-groups via K-theoretic duality for extensions. In particular, we may concretely realize the reciprocal algebra $\\widehat{\\mathcal{O}}_A$ for simple Cuntz--Krieger algebras $\\mathcal{O}_A$. As a result, the algebra $\\widehat{\\mathcal{O}}_A$ is realized as a unital simple purely infinite universal $C^*$-algebra generated by a family of partial isometri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.18126","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/2502.18126/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"}