{"id":"https://openalex.org/W2788198774","doi":"https://doi.org/10.1515/forum-2018-0059","title":"Left semi-braces and solutions of the Yang\u2013Baxter equation","display_name":"Left semi-braces and solutions of the Yang\u2013Baxter equation","publication_year":2018,"publication_date":"2018-10-05","ids":{"openalex":"https://openalex.org/W2788198774","doi":"https://doi.org/10.1515/forum-2018-0059","mag":"2788198774"},"language":"en","primary_location":{"id":"doi:10.1515/forum-2018-0059","doi":"https://doi.org/10.1515/forum-2018-0059","is_oa":false,"landing_page_url":"https://doi.org/10.1515/forum-2018-0059","pdf_url":null,"source":{"id":"https://openalex.org/S64527569","display_name":"Forum Mathematicum","issn_l":"0933-7741","issn":["0933-7741","1435-5337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Forum Mathematicum","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.09993","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022675321","display_name":"Eric Jespers","orcid":"https://orcid.org/0000-0002-2695-7949","observed_orcids":["https://orcid.org/0000-0002-2695-7949"]},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Eric Jespers","raw_affiliation_strings":["Department of Mathematics , Vrije Universiteit Brussel , Pleinlaan 2, 1050 Brussel , Belgium"],"raw_orcid":"https://orcid.org/0000-0002-2695-7949","affiliations":[{"raw_affiliation_string":"Department of Mathematics , Vrije Universiteit Brussel , Pleinlaan 2, 1050 Brussel , Belgium","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087565364","display_name":"Arne Van Antwerpen","orcid":"https://orcid.org/0000-0001-7619-6298","observed_orcids":["https://orcid.org/0000-0001-7619-6298"]},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Arne Van Antwerpen","raw_affiliation_strings":["Department of Mathematics , Vrije Universiteit Brussel , Pleinlaan 2, 1050 Brussel , Belgium"],"raw_orcid":"https://orcid.org/0000-0001-7619-6298","affiliations":[{"raw_affiliation_string":"Department of Mathematics , Vrije Universiteit Brussel , Pleinlaan 2, 1050 Brussel , Belgium","institution_ids":["https://openalex.org/I13469542"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022675321"],"corresponding_institution_ids":["https://openalex.org/I13469542"],"apc_list":{"value":2400,"currency":"EUR","value_usd":2712},"apc_paid":null,"fwci":6.274,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.97991147,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"31","issue":"1","first_page":"241","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.010700000450015068,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/set-theoretic-solutions-of-the-yang-baxter-equation","display_name":"set-theoretic solutions of the Yang-Baxter equation","score":0.8870000243186951},{"id":"https://openalex.org/keywords/non-degenerate-solutions","display_name":"non-degenerate solutions","score":0.6700000166893005},{"id":"https://openalex.org/keywords/degenerate-solutions","display_name":"degenerate solutions","score":0.7979999780654907},{"id":"https://openalex.org/keywords/noetherian-algebras","display_name":"Noetherian algebras","score":0.6840000152587891},{"id":"https://openalex.org/keywords/polynomial-identities","display_name":"polynomial identities","score":0.8579999804496765},{"id":"https://openalex.org/keywords/gelfand-kirillov-dimension","display_name":"Gelfand-Kirillov dimension","score":0.9879999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7614448070526123},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6679686307907104},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.6266810297966003},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6246439814567566},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5896773338317871},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5266011953353882},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5255944728851318},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5182375907897949},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5154372453689575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4981229305267334},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49714234471321106},{"id":"https://openalex.org/C177858542","wikidata":"https://www.wikidata.org/wiki/Q4476530","display_name":"Yang\u2013Baxter equation","level":3,"score":0.47972244024276733},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.4596116244792938},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.45117467641830444},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3439371585845947},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32797977328300476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1594052016735077},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10741403698921204},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1515/forum-2018-0059","doi":"https://doi.org/10.1515/forum-2018-0059","is_oa":false,"landing_page_url":"https://doi.org/10.1515/forum-2018-0059","pdf_url":null,"source":{"id":"https://openalex.org/S64527569","display_name":"Forum Mathematicum","issn_l":"0933-7741","issn":["0933-7741","1435-5337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Forum Mathematicum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.09993","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.09993","pdf_url":"https://arxiv.org/pdf/1802.09993","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:117763","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1802.09993","pdf_url":"https://arxiv.org/pdf/1802.09993","source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2788198774","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.09993.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:archive.ugent.be:01J0XD7ATB0RGBGZFX6N2EX2EW","doi":null,"is_oa":false,"landing_page_url":"https://biblio.ugent.be/publication/01J0XD7ATB0RGBGZFX6N2EX2EW","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1435-5337","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1802.09993","doi":"https://doi.org/10.48550/arxiv.1802.09993","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.09993","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.09993","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.09993","pdf_url":"https://arxiv.org/pdf/1802.09993","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322634","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2788198774.pdf","grobid_xml":"https://content.openalex.org/works/W2788198774.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W166622587","https://openalex.org/W1487875360","https://openalex.org/W1503971394","https://openalex.org/W1571028325","https://openalex.org/W1596655614","https://openalex.org/W1633336122","https://openalex.org/W1781618946","https://openalex.org/W1985885288","https://openalex.org/W1995969674","https://openalex.org/W2007152098","https://openalex.org/W2008345143","https://openalex.org/W2081459283","https://openalex.org/W2090149729","https://openalex.org/W2099697576","https://openalex.org/W2170853108","https://openalex.org/W2274954839","https://openalex.org/W2290687277","https://openalex.org/W2302011925","https://openalex.org/W2414938835","https://openalex.org/W2424997766","https://openalex.org/W2480872961","https://openalex.org/W2606599669","https://openalex.org/W2625398403","https://openalex.org/W2732254484","https://openalex.org/W2963945370","https://openalex.org/W3101270604"],"related_works":["https://openalex.org/W1911648887","https://openalex.org/W3200320046","https://openalex.org/W2606599669","https://openalex.org/W4401520998","https://openalex.org/W7066392797","https://openalex.org/W3195657869","https://openalex.org/W2803904982","https://openalex.org/W4386143151","https://openalex.org/W2252696573","https://openalex.org/W2964052601"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"r":[2,37,62,144],":":[3],"X":[4,7,24,50],"2":[5,8],"\u2192":[6],"{r\\colon":[9],"X^{2}\\rightarrow":[10],"X^{2}}":[11],"be":[12,159,164],"a":[13,21,100,107,151],"set-theoretic":[14],"solution":[15],"of":[16,184],"the":[17,43],"Yang\u2013Baxter":[18],"equation":[19],"on":[20],"finite":[22,128],"set":[23],".":[25],"It":[26],"was":[27],"proven":[28],"by":[29],"Gateva-Ivanova":[30],"and":[31,40,103,111,176,187],"Van":[32],"den":[33],"Bergh":[34],"that":[35,147],"if":[36,60,80],"is":[38,97],"non-degenerate":[39,119],"involutive,":[41],"then":[42,177],"algebra":[44,96],"K":[45],"\u2062":[46,53,57,59,61,63],"\u3008":[47],"x":[48,52,65],"\u2208":[49],"\u2223":[51],"y":[54,67],"=":[55,69],"u":[56,71],"v":[58,73],"(":[64,70],",":[66,72],")":[68,74],"\u3009":[75],"{K\\langle":[76],"x\\in":[77],"X\\mid":[78],"xy=uv\\text{":[79],"}r(x,y)=(u,v)\\rangle}":[81],"shares":[82],"many":[83,91],"properties":[84],"with":[85],"commutative":[86],"polynomial":[87,101],"algebras":[88],"in":[89,93],"finitely":[90],"variables;":[92],"particular,":[94],"this":[95,115,133],"Noetherian,":[98],"satisfies":[99],"identity":[102],"has":[104],"Gelfand\u2013Kirillov":[105],"dimension":[106],"positive":[108],"integer.":[109],"Lebed":[110],"Vendramin":[112],"recently":[113],"extended":[114],"result":[116,140],"to":[117,127,150,168],"arbitrary":[118,142],"bijective":[120],"solutions.":[121],"Such":[122],"solutions":[123,143,157],"are":[124,148],"naturally":[125],"associated":[126,149],"skew":[129],"left":[130,152],"braces.":[131],"In":[132,166],"paper":[134],"we":[135,171],"will":[136],"prove":[137,178],"an":[138],"analogue":[139],"for":[141],"B":[145,154],"{r_{B}}":[146],"semi-brace":[153],";":[155],"such":[156,174],"can":[158,162],"degenerate":[160],"or":[161],"even":[163],"idempotent.":[165],"order":[167],"do":[169],"so,":[170],"first":[172],"describe":[173],"semi-braces":[175],"some":[179],"decompositions":[180],"results":[181],"extending":[182],"those":[183],"Catino,":[185],"Colazzo":[186],"Stefanelli.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2018-03-06T00:00:00"}