{"paper":{"title":"Classification of abelian finite-dimensional $C^*$-algebras by orthogonality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Bojan Kuzma, Sushil Singla","submitted_at":"2024-11-03T20:52:05Z","abstract_excerpt":"The main goal of the article is to prove that if $\\mathcal A_1$ and $\\mathcal A_2$ are Birkhoff-James isomorphic $C^*$-algebras over the fields $\\mathbb F_1$ and $\\mathbb F_2$, respectively and if $\\mathcal A_1$ finite-dimensional, abelian of dimension greater than one, then $\\mathbb F_1=\\mathbb F_2$ and $\\mathcal A_1$ and $\\mathcal A_2$ are (isometrically) $\\ast$-isomorphic $C^*$-algebras. Furthermore, it is also proved that for a finite-dimensional $C^*$-algebra $\\mathcal A$, we have $\\mathcal L_{\\mathcal A}^\\bot$ is the sum of minimal ideals which are not skew-fields and $\\mathcal L_{\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01684","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/2411.01684/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"}