{"paper":{"title":"Simple Witt modules that are finitely generated over the cartan subalgebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Genqiang Liu, Kaiming Zhao, Rencai Lu, Xiangqian Guo","submitted_at":"2017-05-09T15:40:50Z","abstract_excerpt":"Let $d\\ge1$ be an integer, $W_d$ and $\\mathcal{K}_d$ be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=\\mathbb{C} [x_1^{\\pm1}, x_2^{\\pm1}, ..., x_d^{\\pm1}]$, respectively. For any $\\mathfrak{gl}_d$-module $M$ and any admissible module $P$ over the extended Witt algebra $\\widetilde W_d$, we define a $W_d$-module structure on the tensor product $P\\otimes M$. We prove in this paper that any simple $W_d$-module that is finitely generated over the cartan subalgebra is a quotient module of the $W_d$-module $P \\otimes M$ for a finite dimensional simple $\\mathfrak{gl}_d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03393","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/1705.03393/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"}