{"paper":{"title":"Morita equivalences for Zhu's algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Angela Gibney, Chiara Damiolini, Daniel Krashen","submitted_at":"2024-03-18T15:05:25Z","abstract_excerpt":"Through the introduction of new ideals, and with the assistance of the $d$-th mode transition algebras $\\mathfrak{A}_d$, for $d\\in \\mathbb{N}$, we show how Zhu's associative algebra $\\mathsf{A}$, conventionally valued for tracking information about the degree $0$ part of an $\\mathbb{N}$-graded module over a vertex operator algebra $V$, also contains information about components of higher degree. As an application, equivalent conditions are given for rationality of $V$, and explicit presentations for higher-level Zhu algebras are given, including for a large class of non-rational VOAs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11855","kind":"arxiv","version":3},"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/2403.11855/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"}