{"paper":{"title":"Equivalence Relations on Vertex Operator Algebras, I: Genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Brandon C. Rayhaun, Sven M\\\"oller","submitted_at":"2024-08-13T18:00:00Z","abstract_excerpt":"In this first of a series of two papers, we investigate two different equivalence relations obtained by generalizing the notion of genus of even lattices to the setting of vertex operator algebras (or two-dimensional chiral algebras). The bulk genus equivalence relation was defined in arXiv:math/0209333 and groups (suitably regular) vertex operator algebras according to their modular tensor category and central charge. Hyperbolic genus arXiv:2004.01441 tests isomorphy after tensoring with a hyperbolic plane vertex algebra. Physically, two rational chiral algebras are said to belong to the same"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07117","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/2408.07117/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"}