{"paper":{"title":"The diagonal dimension of sub-C*-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Hung-Chang Liao, Kang Li, Wilhelm Winter","submitted_at":"2023-03-29T14:57:34Z","abstract_excerpt":"We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C*-algebras (sometimes also referred to as diagonal C*-pairs). Our concept has good permanence properties and detects more refined information than nuclear dimension. In many situations it is precisely how dynamical information is encoded in an associated C*-pair.\n  For free actions on compact Hausdorff spaces, diagonal dimension of the crossed product with its canonical diagonal is bounded above by a product involving Kerr's tower dimension of the action and covering dimension of the space. It is bounded below by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16762","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/2303.16762/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"}