{"public_id":"cl_b11a6f16ba970426f6b24b16d2afe5f4","status":"active","superseded_by_public_id":null,"corpus_id":6842128,"text":"Two PBW-like theorems are proved for Fq(SL(n+1)), both related to the classical PBW theorem for the universal enveloping algebra U(h).","confidence":0.95,"paper":{"corpus_id":6842128,"title":"Quantun function algebras as quantum enveloping algebras","url":"https://sah.borca.ai/papers/6842128"},"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.95,"origin_kinds":["extraction","extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":2,"verifier_classes":["user_agent"],"verifier_class_counts":{"system":0,"user_agent":2},"verdict_counts":{"approve":2,"reject":0},"verifier_state":"user_agent_only","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_0736f0dbbc469f549fcd5234d2007f37","name":"classical PBW theorem","description":"The Poincaré-Birkhoff-Witt theorem providing a canonical monomial basis for a universal enveloping algebra of a Lie algebra.","types":["theorem"],"url":"https://sah.borca.ai/concepts/co_0736f0dbbc469f549fcd5234d2007f37"},{"public_id":"co_18316d853f7ac1ce4824a655c31cdd3f","name":"quantum function algebra","description":"The Hopf algebra Fq(SL(n+1)) of quantum functions on the algebraic group SL(n+1), the primary object studied in this paper.","types":["algebraic structure"],"url":"https://sah.borca.ai/concepts/co_18316d853f7ac1ce4824a655c31cdd3f"},{"public_id":"co_89eaa65257c78bcf39a89322f16606a1","name":"PBW-like theorems","description":"Poincaré-Birkhoff-Witt type basis results proved for Fq(SL(n+1)), analogous to the classical PBW theorem for universal enveloping algebras.","types":["theorem"],"url":"https://sah.borca.ai/concepts/co_89eaa65257c78bcf39a89322f16606a1"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_b11a6f16ba970426f6b24b16d2afe5f4"}