{"paper":{"title":"The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Masaki Izumi, Taro Sogabe","submitted_at":"2019-03-12T10:05:33Z","abstract_excerpt":"We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra $O_{n+1}$ for finite n in terms of K-theory. We show that there is an example of a space for which the homotopy set is a non-commutative group, and hence the classifying space of the automorphism group of the Cuntz algebra for finite n is not an H-space. We also make an improvement of Dadarlat's classification of continuous fields of the Cuntz algebras in terms of vector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04809","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"}