{"paper":{"title":"Stable rank of $\\mathrm{C}(X)\\rtimes\\Gamma$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Chun Guang Li, Zhuang Niu","submitted_at":"2020-08-07T20:11:55Z","abstract_excerpt":"It is shown that, for an arbitrary free and minimal $\\mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $\\mathrm{C}(X)\\rtimes\\mathbb Z^n$ always has stable rank one, i.e., invertible elements are dense. This generalizes a result of Alboiu and Lutley on $\\mathbb Z$-actions.\n  In fact, for any free and minimal topological dynamical system $(X, \\Gamma)$, where $\\Gamma$ is a countable discrete amenable group, if it has the uniform Rokhlin property and Cuntz comparison of open sets, then the crossed product C*-algebra $\\mathrm{C}(X)\\rtimes\\Gamma$ has stable rank on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.03361","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/2008.03361/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"}