{"paper":{"title":"Tilting Modules in Truncated Categories","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Angelo Bianchi, Matthew Bennett","submitted_at":"2013-07-12T03:02:54Z","abstract_excerpt":"We begin the study of a tilting theory in certain truncated categories of modules $\\mathcal G(\\Gamma)$ for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where $\\Gamma = P^+ \\times J$, $J$ is an interval in $\\mathbb Z$, and $P^+$ is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category $\\mathcal G(\\Gamma')$ where $\\Gamma' = P' \\times J$, where $P'\\subseteq P^+$ is saturated. Under certain natural conditions on $\\Gamma'$, we note that $\\mathcal G(\\Gamma')$ admits full tilting modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3307","kind":"arxiv","version":7},"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"}