{"paper":{"title":"Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Andreas N{\\ae}s Aaserud, David E. Evans","submitted_at":"2019-08-07T15:10:33Z","abstract_excerpt":"We associate to each Temperley-Lieb-Jones C*-tensor category $\\mathcal{T}\\!\\mathcal{L}\\mathcal{J}(\\delta)$ with parameter $\\delta$ in the discrete range $\\{2\\cos(\\pi/(k+2))\\,:\\,k=1,2,\\ldots\\}\\cup\\{2\\}$ a certain C*-algebra $\\mathcal{B}$ of compact operators. We use the unitary braiding on $\\mathcal{T}\\!\\mathcal{L}\\mathcal{J}(\\delta)$ to equip the category $\\mathrm{Mod}_{\\mathcal{B}}$ of (right) Hilbert $\\mathcal{B}$-modules with the structure of a braided C*-tensor category. We show that $\\mathcal{T}\\!\\mathcal{L}\\mathcal{J}(\\delta)$ is equivalent, as a braided C*-tensor category, to the full s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02674","kind":"arxiv","version":3},"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/1908.02674/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"}