{"paper":{"title":"Axiomatic framework for the BGG Category O","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Apoorva Khare","submitted_at":"2015-02-24T08:11:13Z","abstract_excerpt":"We introduce a general axiomatic framework for algebras with triangular decomposition, which allows for a systematic study of the Bernstein-Gelfand-Gelfand Category $\\mathcal{O}$. The framework is stated via three relatively simple axioms; algebras satisfying them are termed \"regular triangular algebras (RTAs)\". These encompass a large class of algebras in the literature, including (a) generalized Weyl algebras, (b) symmetrizable Kac-Moody Lie algebras $\\mathfrak{g}$, (c) quantum groups $U_q(\\mathfrak{g})$ over \"lattices with possible torsion\", (d) infinitesimal Hecke algebras, (e) higher rank"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06706","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"}