{"paper":{"title":"Forced gradings in integral quasi-hereditary algebras with applications to quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2012-03-07T17:36:10Z","abstract_excerpt":"Let $\\sO$ be a discrete valuation ring with fraction field $K$ and residue field $k$. A quasi-hereditary algebra $\\wA$ over $\\sO$ provides a bridge between the representation theory of the quasi-hereditary algebra $\\wA_K:=K\\otimes \\wA$ over the field $K$ and the quasi-hereditary algebra $A_k:=k\\otimes_\\sO\\wA$ over $k$. In one important example, $\\wA_K$--mod is a full subcategory of the category of modules for a quantum enveloping algebra while $\\wA_k$--mod is a full subcategory of the category of modules for a reductive group in positive characteristic. This paper considers first the question "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1550","kind":"arxiv","version":2},"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"}