{"paper":{"title":"Classification of $\\mathbb{Z}/2\\mathbb{Z}$-quadratic unitary fusion categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CT","math.OA"],"primary_cat":"math.QA","authors_text":"Cain Edie-Michell, David Penneys, Masaki Izumi","submitted_at":"2021-08-03T15:20:39Z","abstract_excerpt":"A unitary fusion category is called $\\mathbb{Z}/2\\mathbb{Z}$-quadratic if it has a $\\mathbb{Z}/2\\mathbb{Z}$ group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of $\\mathbb{Z}/2\\mathbb{Z}$-quadratic unitary fusion categories. The main tools for this classification are skein theory, a generalization of Ostrik's results on formal codegrees to analyze the induction of the group elements to the center, and a computation similar to Larson's rank-finiteness bound for $\\mathbb{Z}/3\\mathbb{Z}$-near group pseudounitary fusio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01564","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.01564/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"}