{"paper":{"title":"Finiteness and Construction of Internal Hom for Vertex Operator Algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Chao Yang, Yiyi Zhu","submitted_at":"2026-06-20T16:25:40Z","abstract_excerpt":"Let $V$ be a vertex operator algebra, and let $W^1$ and $W^2$ be restricted $V$-modules. We construct a generalized $V$-module $\\mathcal{H}(W^1, W^2)$ characterized by canonical universal properties. We show that, under suitable hypotheses, $ \\mathcal{H}(W^1, W^2)$ realizes the internal Hom object in the tensor category of restricted $V$-modules. Although our construction differs from Li's, we show that it agrees with the natural logarithmic generalization of Li's module $\\Delta(W^1, W^2)$. We further establish a canonical isomorphism between $\\mathcal{H} \\big(W^1,(W^2 )^\\prime \\big)$ and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22135","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/2606.22135/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"}