{"paper":{"title":"Perforation conditions and almost algebraic order in Cuntz semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Francesc Perera, Henning Petzka, Ramon Antoine","submitted_at":"2016-04-22T15:47:17Z","abstract_excerpt":"For a C$^*$-algebra $A$, it is an important problem to determine the Cuntz semigroup $\\mathrm{Cu}(A\\otimes\\mathcal{Z})$ in terms of $\\mathrm{Cu}(A)$. We approach this problem from the point of view of semigroup tensor products in the category of abstract Cuntz semigroups, by analysing the passage of significant properties from $\\mathrm{Cu}(A)$ to $\\mathrm{Cu}(A)\\otimes_\\mathrm{Cu}\\mathrm{Cu}(\\mathcal{Z})$. We describe the effect of the natural map $\\mathrm{Cu}(A)\\to\\mathrm{Cu}(A)\\otimes_\\mathrm{Cu}\\mathrm{Cu}(\\mathcal{Z})$ in the order of $\\mathrm{Cu}(A)$, and show that, if $A$ has real rank z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06718","kind":"arxiv","version":3},"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"}