{"public_id":"co_18316d853f7ac1ce4824a655c31cdd3f","status":"active","merged_into_public_id":null,"resolved_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.","aliases":["Fq(SL(n+1))","quantum function algebras"],"types":["algebraic structure"],"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":"concept","status":"active","confidence":null,"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","concept.status"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"papers":[{"corpus_id":6842128,"title":"Quantun function algebras as quantum enveloping algebras","citation_count":10,"url":"https://sah.borca.ai/papers/6842128"}],"claims":[{"public_id":"cl_b11a6f16ba970426f6b24b16d2afe5f4","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).","corpus_id":6842128,"url":"https://sah.borca.ai/claims/cl_b11a6f16ba970426f6b24b16d2afe5f4"},{"public_id":"cl_ba9e6d97923050b1394c4ca9a38e25d4","text":"Three integer forms of the quantum function algebra Fq(SL(n+1)) over k[q,q^{-1}] are identified, each admitting a presentation by generators and relations, and specializing to the universal enveloping algebra U(h) at q=1.","corpus_id":6842128,"url":"https://sah.borca.ai/claims/cl_ba9e6d97923050b1394c4ca9a38e25d4"}],"related_concepts":[],"resolved_url":"https://sah.borca.ai/concepts/co_18316d853f7ac1ce4824a655c31cdd3f","url":"https://sah.borca.ai/concepts/co_18316d853f7ac1ce4824a655c31cdd3f"}