{"paper":{"title":"Vertex Operator Algebras with Two Simple Modules - the Mathur-Mukhi-Sen Theorem Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Geoffrey Mason, Kiyokazu Nagatomo, Yuichi Sakai","submitted_at":"2018-03-29T23:16:53Z","abstract_excerpt":"Let $V$ be a strongly regular vertex operator algebra and let $\\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\\ It is known that $\\frak{ch}_V$ is the space of solutions of a so-called \\emph{modular linear differential equation (MLDE)}.\\ In this paper we obtain a near-classification of those $V$ for which the corresponding MLDE is irreducible and monic of order $2$.\\ As a consequence we derive the complete classification when $V$ has exactly two simple modules.\\ It turns out that $V$ is either one of four affine Kac-Moody algebras of level $1$, or the Yang-Le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11281","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":""},"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"}