{"paper":{"title":"Higher level Zhu algebras and modules for vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Jinwei Yang, Katrina Barron, Nathan Vander Werf","submitted_at":"2017-10-13T01:07:41Z","abstract_excerpt":"Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra $V$, we study the relationship between various types of $V$-modules and modules for the higher level Zhu algebras for $V$, denoted $A_n(V)$, for $n \\in \\mathbb{N}$, first introduced by Dong, Li, and Mason in 1998. We resolve some issues that arise in a few theorems previously presented when these algebras were first introduced, and give examples illustrating the need for certain modifications of the statements of those theorems. We establish that whether or not $A_{n-1}(V)$ is isomorphic to a direct summa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04767","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":""},"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"}