{"paper":{"title":"Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.OA","authors_text":"Andreas Doering","submitted_at":"2012-12-11T20:29:46Z","abstract_excerpt":"To each unital C*-algebra A we associate a presheaf \\Sigma^A, called the spectral presheaf of A, which can be regarded as a generalised Gelfand spectrum. We develop a categorical notion of local duality and show that there is a contravariant functor from the category of unital C*-algebras to a suitable category of presheaves containing the spectral presheaves. We clarify how much algebraic information about a C*-algebra is contained in its spectral presheaf. A nonabelian unital C*-algebra A that is neither isomorphic to C^2 nor to B(C^2) is determined by its spectral presheaf up to quasi-Jorda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2613","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":""},"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"}