{"paper":{"title":"K_1-injectivity for properly infinite C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Etienne Blanchard","submitted_at":"2008-04-29T14:33:46Z","abstract_excerpt":"One of the main tools to classify \\cst-algebras is the study of its projections and its unitaries. It was proved by Cuntz in \\cite{Cu81} that if $A$ is a \\textit{purely infinite} simple \\cst-algebra, then the kernel of the natural map for the unitary group $\\U(A)$ to the $K$-theory group $K_1(A)$ is reduced to the connected component $\\U^0(A)$, i.e. $A$ is \\textit{$K_1$-injective} (see \\S 3). We study in this note a finitely generated \\cst-algebra, the $K_1$-injectivity of which would imply the $K_1$-injectivity of all unital \\textit{properly infinite} \\cst-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4624","kind":"arxiv","version":13},"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"}