{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QQX6HG7GUEFGITABYKDLI4JPRA","short_pith_number":"pith:QQX6HG7G","schema_version":"1.0","canonical_sha256":"842fe39be6a10a644c01c286b4712f8811a3fd7f2e523941598263ce86496b4a","source":{"kind":"arxiv","id":"1507.05894","version":2},"attestation_state":"computed","paper":{"title":"On Category $\\mathcal{O}$ over triangular Generalized Weyl Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Akaki Tikaradze, Apoorva Khare","submitted_at":"2015-07-21T16:21:16Z","abstract_excerpt":"We analyze the BGG Category $\\mathcal{O}$ over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a \"triangular\" GWA for which Category $\\mathcal{O}$ decomposes into a direct sum of subcategories, we study in detail the homological properties of blocks with finitely many simples. As consequences, we show that the endomorphism algebra of a projective generator of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We also classify all tilting modules in the block, as well as all submodules of all projective and tilting modules. Finally, we prese"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.05894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-21T16:21:16Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"0b117194f65c59eb71f9640edd32897072af676c2d07b3e7816eee2c443fd129","abstract_canon_sha256":"8e756d3d7c9f5c979411e6f4ac89bc267769f8901adcc7f02ff09469ca2f6064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:49.008280Z","signature_b64":"8wrTnnzMZRNx83SK+Vl8WKzZWgZC0jSljPThDNE1SLqZT/j2VURA0FIdYTnU/BdIKBqoMtXFVvVfhMf5CTViAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"842fe39be6a10a644c01c286b4712f8811a3fd7f2e523941598263ce86496b4a","last_reissued_at":"2026-05-18T01:23:49.007698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:49.007698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Category $\\mathcal{O}$ over triangular Generalized Weyl Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Akaki Tikaradze, Apoorva Khare","submitted_at":"2015-07-21T16:21:16Z","abstract_excerpt":"We analyze the BGG Category $\\mathcal{O}$ over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a \"triangular\" GWA for which Category $\\mathcal{O}$ decomposes into a direct sum of subcategories, we study in detail the homological properties of blocks with finitely many simples. As consequences, we show that the endomorphism algebra of a projective generator of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We also classify all tilting modules in the block, as well as all submodules of all projective and tilting modules. Finally, we prese"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05894","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.05894","created_at":"2026-05-18T01:23:49.007790+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05894v2","created_at":"2026-05-18T01:23:49.007790+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05894","created_at":"2026-05-18T01:23:49.007790+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQX6HG7GUEFG","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQX6HG7GUEFGITAB","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQX6HG7G","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA","json":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA.json","graph_json":"https://pith.science/api/pith-number/QQX6HG7GUEFGITABYKDLI4JPRA/graph.json","events_json":"https://pith.science/api/pith-number/QQX6HG7GUEFGITABYKDLI4JPRA/events.json","paper":"https://pith.science/paper/QQX6HG7G"},"agent_actions":{"view_html":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA","download_json":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA.json","view_paper":"https://pith.science/paper/QQX6HG7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05894&json=true","fetch_graph":"https://pith.science/api/pith-number/QQX6HG7GUEFGITABYKDLI4JPRA/graph.json","fetch_events":"https://pith.science/api/pith-number/QQX6HG7GUEFGITABYKDLI4JPRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA/action/storage_attestation","attest_author":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA/action/author_attestation","sign_citation":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA/action/citation_signature","submit_replication":"https://pith.science/pith/QQX6HG7GUEFGITABYKDLI4JPRA/action/replication_record"}},"created_at":"2026-05-18T01:23:49.007790+00:00","updated_at":"2026-05-18T01:23:49.007790+00:00"}