{"paper":{"title":"Conjugacy and cocycle conjugacy of automorphisms of $\\mathcal{O}_{2}$ are not Borel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Eusebio Gardella, Martino Lupini","submitted_at":"2014-04-14T15:17:23Z","abstract_excerpt":"The group of automorphisms of the Cuntz algebra $\\mathcal{O}_{2}$ is a Polish group with respect to the topology of pointwise convergence in norm. Our main result is that the relations of conjugacy and cocycle conjugacy of automorphisms of $\\mathcal{O}_{2}$ are complete analytic sets and, in particular, not Borel. Moreover, we show that from the point of view of Borel complexity theory, classifying automorphisms of $\\mathcal{O}_{2}$ up to conjugacy or cocycle conjugacy is strictly more difficult than classifying up to isomorphism any class of countable structures with Borel isomorphism relatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3617","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"}