{"paper":{"title":"Hereditary C*-Subalgebra Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.OA","authors_text":"Charles A. Akemann, Tristan Bice","submitted_at":"2014-10-01T02:23:22Z","abstract_excerpt":"We investigate the connections between order and algebra in the hereditary C*-subalgebra lattice $\\mathcal{H}(A)$ and *-annihilator ortholattice $\\mathscr{P}(A)^\\perp$. In particular, we characterize $\\vee$-distributive elements of $\\mathcal{H}(A)$ as ideals, answering a 25 year old question, allowing the quantale structure of $\\mathcal{H}(A)$ to be completely determined from its lattice structure. We also show that $\\mathscr{P}(A)^\\perp$ is separative, allowing for C*-algebra type decompositions which are completely consistent with the original von Neumann algebra type decompositions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0093","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":""},"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"}