{"paper":{"title":"Simple Toroidal Vertex Algebras and Their Irreducible Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Fei Kong, Haisheng Li, Qing Wang, Shaobin Tan","submitted_at":"2014-08-04T04:07:11Z","abstract_excerpt":"In this paper, we continue the study on toroidal vertex algebras initiated in \\cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(\\hat{\\frak{g}})=\\hat{\\frak{g}}\\otimes L_r$, where $\\hat{\\frak{g}}$ is an untwisted affine Lie algebra and $L_r=$\\mathbb{C}[t_{1}^{\\pm 1},\\ldots,t_{r}^{\\pm 1}]$. We first construct an $(r+1)$-toroidal vertex algebra $V(T,0)$ and show that the category of restricted $L_{r}(\\hat{\\frak{g}})$-modules is canonically isomorphic to that of $V(T,0)$-modules.Let $c$ denote the standard central element of $\\hat{\\frak{g}}$ and set $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0579","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"}