{"corpus_id":6842128,"paper_sha":"5cf3ddc8d3d9e5c9cd14b6a10c070a7d2fd8c63d","doi":"10.1080/00927879808826240","arxiv_id":"q-alg/9701010","pmid":null,"pmcid":null,"mag_id":3104539531,"dblp_id":null,"acl_id":null,"title":"Quantun function algebras as quantum enveloping algebras","year":1997,"publication_date":"1997-01-10","venue":"","journal":{"name":"Communications in Algebra","pages":"1795-1818","volume":"26"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":16,"citation_count":10,"influential_citation_count":1,"is_open_access":true,"arxiv_categories":["q-alg","math.QA"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":"Communications in Algebra 26, no. 6 (1998), 1795-1818","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"http://arxiv.org/pdf/q-alg/9701010","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/5cf3ddc8d3d9e5c9cd14b6a10c070a7d2fd8c63d","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Inspired by a result in (Ga), we locate three integer forms of Fq(SL(n + 1)) over k ( q;q 1 ) , with a presentation by generators and relations, which for q = 1 specialize to U(h), where h is the Lie bialgebra of the Poisson Lie group dual to SL(n + 1). In sight of this we prove two PBW-like theorems for Fq(SL(n + 1)), both related to the classical PBW theorem for U(h).","claims":[{"public_id":"cl_ba9e6d97923050b1394c4ca9a38e25d4","status":"active","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.","confidence":0.93,"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 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