{"paper":{"title":"Smooth and non-smooth $AF$-algebras and problem on invariant measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Anatoly Vershik","submitted_at":"2013-04-08T12:55:43Z","abstract_excerpt":"We separate the $AF$-algebras (correspondingly action of the countable groups on Cantor sets) onto two classes ---- \"completely smooth\" for which the set of all indecomposable traces (correspondingly list of all invariant ergodic measures) has nice parametrization, and the second class --- \"completely non-smooth\" for which the set of all traces (correspondingly set of all invariant measures) is Poulsen simplex and therefore there is no suitable parametrization of indecomposable traces, (ergodic measures) e.g.Choquet boundary.\n  Important example of the first type of $AF$-algebra is group algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2193","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"}