{"paper":{"title":"Projective modules over classical Lie algebras of infinite rank in the parabolic category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chih-Whi Chen, Ngau Lam","submitted_at":"2018-02-06T18:19:41Z","abstract_excerpt":"We study the truncation functors and show the existence of projective cover of each irreducible module in parabolic BGG category $\\mathcal O$ over infinite rank Lie algebra of types $\\mathfrak{a,b,c,d}$. Moreover, $\\mathcal O$ is a Koszul category. As a consequence, the corresponding parabolic BGG category $\\overline{\\mathcal O}$ over infinite rank Lie superalgebra of types $\\mathfrak{a,b,c,d}$ through the super duality is also a Koszul category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02112","kind":"arxiv","version":3},"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"}