{"paper":{"title":"Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kevin Aguyar Brix, Toke Meier Carlsen","submitted_at":"2017-12-01T03:54:19Z","abstract_excerpt":"A one-sided shift of finite type $(X_A,\\sigma_A)$ determines on the one hand a Cuntz-Krieger algebra $\\mathcal{O}_A$ with a distinguished abelian subalgebra $\\mathcal{D}_A$ and a certain completely positive map $\\tau_A$ on $\\mathcal{O}_A$. On the other hand, $(X_A,\\sigma_A)$ determines a groupoid $\\mathcal{G}_A$ together with a certain homomorphism $\\epsilon_A$ on $\\mathcal{G}_A$. We show that this data completely characterizes the one-sided conjugacy class of $X_A$. This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00179","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1712.00179/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"}