{"paper":{"title":"Structure and $K$-theory of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Kang Li, Yeong Chyuan Chung","submitted_at":"2019-04-15T13:56:49Z","abstract_excerpt":"In this paper, we characterize when the $\\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\\in [1,\\infty)$. Moreover, we show that the $\\ell^p$ uniform Roe algebra is a (non-sequential) spatial $L^p$ AF algebra in the sense of Phillips and Viola if and only if the underlying metric space has asymptotic dimension zero.\n  We also consider the ordered $K_0$ groups of $\\ell^p$ uniform Roe algebras for metric spaces with low asymptotic dimension, showing that (1) the ordered $K_0$ group is trivial when the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07050","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"}