{"paper":{"title":"Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Pere Ara, Ruy Exel","submitted_at":"2012-10-25T18:08:22Z","abstract_excerpt":"We attach to each finite bipartite separated graph (E,C) a partial dynamical system (\\Omega(E,C), F, \\theta), where \\Omega(E,C) is a zero-dimensional metrizable compact space, F is a finitely generated free group, and {\\theta} is a continuous partial action of F on \\Omega(E,C). The full crossed product C*-algebra O(E,C) = C(\\Omega(E,C)) \\rtimes_{\\theta} F is shown to be a canonical quotient of the graph C*-algebra C^*(E,C) of the separated graph (E,C). Similarly, we prove that, for any *-field K, the algebraic crossed product L^{ab}_K(E,C) = C_K(\\Omega(E,C)) \\rtimes_\\theta^{alg} F is a canonic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6931","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":""},"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"}