{"paper":{"title":"Computable $K$-theory for $\\mathrm{C}^*$-algebras: UHF algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.LO","authors_text":"Christopher Eagle, Isaac Goldbring, Russell Miller, Timothy McNicholl","submitted_at":"2025-01-15T02:35:35Z","abstract_excerpt":"We initiate the study of the effective content of $K$-theory for $\\mathrm{C}^*$-algebras. We prove that there are computable functors which associate, to a computably enumerable presentation of a $\\mathrm{C}^*$-algebra $\\boldA$, computably enumerable presentations of the abelian groups $K_0(\\boldA)$ and $K_1(\\boldA)$. When $\\boldA$ is stably finite, we show that the positive cone of $K_0(\\boldA)$ is computably enumerable. We strengthen the results in the case that $\\boldA$ is a UHF algebra by showing that the aforementioned presentation of $K_0(\\boldA)$ is actually computable. In the UHF case,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08526","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08526/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"}