{"paper":{"title":"Representations of Conformal Nets, Universal C*-Algebras and K-Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.KT","math.MP"],"primary_cat":"math.OA","authors_text":"Mihaly Weiner, Roberto Conti, Robin Hillier, Sebastiano Carpi","submitted_at":"2012-02-12T16:28:28Z","abstract_excerpt":"We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the split property then, for every representation \\pi of A with finite statistical dimension, \\pi(C*(A)) is weakly closed and hence a finite direct sum of type I_\\infty factors. We define the more manageable locally normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2543","kind":"arxiv","version":4},"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"}