{"paper":{"title":"Some categories of modules for toroidal Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hongyan Guo, Qing Wang, Shaobin Tan","submitted_at":"2013-09-06T03:35:40Z","abstract_excerpt":"In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\\tau$. More specifically, we define and study two categories $\\mathcal{E}_{\\tau}$ and $\\mathcal{C}_{\\tau}$ of $\\tau$-modules using generating functions, where $\\mathcal{E}_{\\tau}$ is proved to contain the evaluation modules while $\\mathcal{C}_{\\tau}$ contains certain restricted $\\tau$-modules, the evaluation modules, and their tensor product modules. Furthermore, we classify the irreducible integrable modules in categories $\\mathcal{E}_{\\tau}$ and $\\mathcal{C}_{\\tau}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1530","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"}