{"paper":{"title":"Coronas and strongly self-absorbing C*-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"G\\'abor Szab\\'o, Ilijas Farah","submitted_at":"2024-11-04T17:05:32Z","abstract_excerpt":"Let $\\mathcal D$ be a strongly self-absorbing $\\mathrm{C}^*$-algebra. Given any separable $\\mathrm{C}^*$-algebra $A$, our two main results assert the following. If $A$ is $\\mathcal D$-stable, then the corona algebra of $A$ is $\\mathcal D$-saturated, i.e., $\\mathcal D$ embeds unitally into the relative commutant of every separable $\\mathrm{C}^*$-subalgebra. Conversely, assuming that the stable corona of $A$ is separably $\\mathcal D$-stable, we prove that $A$ is $\\mathcal D$-stable. This generalizes recent work by the first-named author on the structure of the Calkin algebra. As an immediate cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02274","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}