{"paper":{"title":"On the invariant uniform Roe algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Otgonbayar Uuye, Takeshi Katsura","submitted_at":"2012-11-07T10:14:50Z","abstract_excerpt":"Let $\\Gamma$ be a countable discrete group. We show that $\\Gamma$ has the approximation property if and only if $\\Gamma$ is exact and for any operator space $S \\subseteq \\K(H)$ we have $\\Cu(\\Gamma)^{\\Gamma} \\otimes S = (\\Cu(\\Gamma) \\otimes S)^{\\Gamma}$, where $\\Cu(\\Gamma)$ is the uniform Roe algebra with the right adjoint $\\Gamma$-action. This answers a question of J. Zacharias. We also show that characterisations of several properties of $\\Gamma$ in terms of the reduced group \\cast-algebra apply to the invariant uniform Roe algebra $\\Cu(\\Gamma)^{\\Gamma}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1501","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":""},"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"}