{"paper":{"title":"Operator Algebras of Universal Quantum Homomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Issan Patri, Malay Mandal, Pierre Fima","submitted_at":"2024-11-28T15:12:24Z","abstract_excerpt":"Given two unital C*-algebras $A$ and $B$, we study, when it exists, the universal unital $C^*$-algebra $\\mathcal{U}(A,B)$ generated by the coefficients of a unital $*$-homomorphism $\\rho\\,:\\, A\\rightarrow B\\otimes\\mathcal{U}(A,B)$. When $B$ is finite dimensional, it is well known that $\\mathcal{U}(A,B)$ exists and we study in this case properties LP, RFD, primitiveness and the UCT as well as $K$-theory. We also construct a reduced version of $\\mathcal{U}(A,B)$ for which we study exactness, nuclearity, simplicity, absence of non-trivial projection and $K$-theory. Then, we consider the von Neuma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19199","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/2411.19199/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"}