{"id":"https://openalex.org/W1631981124","doi":"https://doi.org/10.48550/arxiv.math/0405477","title":"Jordanian Quantum (Super)Algebras $U_{h}(g)$ via Contraction Method and Mapping:Review","display_name":"Jordanian Quantum (Super)Algebras $U_{h}(g)$ via Contraction Method and Mapping:Review","publication_year":2004,"publication_date":"2004-05-25","ids":{"openalex":"https://openalex.org/W1631981124","doi":"https://doi.org/10.48550/arxiv.math/0405477","mag":"1631981124"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:math/0405477","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0405477","pdf_url":"https://arxiv.org/pdf/math/0405477","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"},"parent_works":[],"lineage":["https://openalex.org/W1631981124"],"child_works_count":0,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0405477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025699905","display_name":"B. Abdesselam","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I137407579","display_name":"Universit\u00e9 Oran 1 Ahmed Ben Bella","ror":"https://ror.org/059et2b68","country_code":"DZ","type":"education","lineage":["https://openalex.org/I137407579"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Abdesselam, B.","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique d'Oran , Universit d'Oran Es-S\u00e9nia , 31100- Oran , Alg\u00e9rie"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique d'Oran , Universit d'Oran Es-S\u00e9nia , 31100- Oran , Alg\u00e9rie","institution_ids":["https://openalex.org/I137407579"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056155593","display_name":"R. Chakrabarti","orcid":"https://orcid.org/0000-0003-4616-955X","observed_orcids":["https://orcid.org/0000-0003-4616-955X"]},"institutions":[{"id":"https://openalex.org/I215927","display_name":"University of Madras","ror":"https://ror.org/04jmt9361","country_code":"IN","type":"education","lineage":["https://openalex.org/I215927"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Chakrabarti, R.","raw_affiliation_strings":["Department of Theoretical Physics , University of Madras , Guindy Campus , Madras 600025 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Physics , University of Madras , Guindy Campus , Madras 600025 , India","institution_ids":["https://openalex.org/I215927"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040897956","display_name":"Abdelkader Yanallah","orcid":"https://orcid.org/0000-0003-3790-5535","observed_orcids":["https://orcid.org/0000-0003-3790-5535"]},"institutions":[{"id":"https://openalex.org/I4210124230","display_name":"Universit\u00e9 Mustapha Stambouli de Mascara","ror":"https://ror.org/02vqddp65","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210124230"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Yanallah, A.","raw_affiliation_strings":["Laboratoire de Physique Quantique de la Mati\u00e8re et Mod\u00e9lisations Math\u00e9matiques (LPQ3M) , Centre Universitaire de Mascara , 29000- Mascara , Alg\u00e9rie"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Quantique de la Mati\u00e8re et Mod\u00e9lisations Math\u00e9matiques (LPQ3M) , Centre Universitaire de Mascara , 29000- Mascara , Alg\u00e9rie","institution_ids":["https://openalex.org/I4210124230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064353144","display_name":"Mohammed Brahim Zahaf","orcid":"https://orcid.org/0000-0002-4611-9299","observed_orcids":["https://orcid.org/0000-0002-4611-9299"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zahaf, M. B.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9326000213623047,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9326000213623047,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.05959999933838844,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/quantum-superalgebras","display_name":"quantum superalgebras","score":0.8379999995231628},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.7139999866485596},{"id":"https://openalex.org/keywords/coalgebra-structure","display_name":"coalgebra structure","score":0.7829999923706055}],"concepts":[{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.7593008279800415},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5393362641334534},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.4446646273136139},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4340288043022156},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4325481057167053},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.43184250593185425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4091184139251709},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3509831726551056},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3356848955154419},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11316573619842529},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:math/0405477","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0405477","pdf_url":"https://arxiv.org/pdf/math/0405477","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":"doi:10.48550/arxiv.math/0405477","doi":"https://doi.org/10.48550/arxiv.math/0405477","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0405477","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:math/0405477","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0405477","pdf_url":"https://arxiv.org/pdf/math/0405477","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1631981124.pdf","grobid_xml":"https://content.openalex.org/works/W1631981124.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W98515915","https://openalex.org/W1519060719","https://openalex.org/W1661352576","https://openalex.org/W1853569041","https://openalex.org/W1964262369","https://openalex.org/W1985874234","https://openalex.org/W2059932033","https://openalex.org/W2594607422","https://openalex.org/W2612451553","https://openalex.org/W2963322157","https://openalex.org/W3098724327","https://openalex.org/W3102371674"],"related_works":["https://openalex.org/W7098361328","https://openalex.org/W6966514097","https://openalex.org/W1865091466","https://openalex.org/W1860814737","https://openalex.org/W2964336765","https://openalex.org/W7100668456","https://openalex.org/W7100829998","https://openalex.org/W1853569041","https://openalex.org/W3103501240"],"abstract_inverted_index":{"Recently,":[0],"a":[1,38,91,136],"class":[2],"of":[3,5,54,57,94],"transformations":[4],"$R_q$-matrices":[6],"was":[7],"introduced":[8],"such":[9],"that":[10,44],"the":[11,30,33,95,99,110,120,148],"$q":[12,26],"\\to":[13,27],"1$":[14],"limit":[15],"gives":[16],"explicit":[17],"nonstandard":[18,121],"$R_h$-matrices.":[19],"The":[20,157],"transformation":[21],"matrix":[22,77],"is":[23],"singular":[24],"as":[25],"1$.":[28],"For":[29],"transformed":[31],"matrix,":[32],"singularities,":[34],"however,":[35],"cancel":[36],"yielding":[37],"well-defined":[39],"construction.":[40],"We":[41],"have":[42],"shown":[43],"our":[45,142],"method":[46,85],"can":[47,105],"be":[48,106],"implemented":[49],"systematically":[50],"on":[51,98,144],"$R_q$":[52,76],"matrices":[53,160],"all":[55,155],"dimensions":[56],"$U_q(sl(N)),":[58],"U_Q(osp(1|2))$":[59],"and":[60,71,128],"$U_q(sl(2|1))$":[61,72],"algebras.":[62],"Explicit":[63],"constructions":[64],"are":[65,133,161],"presented":[66],"for":[67,78,154],"$U_q(sl(2)),":[68],"U_q(sl(3)),":[69],"U_q(osp(1|2))$":[70],"algebras,":[73],"while":[74],"choosing":[75],"(fund.":[79],"rep.)":[80],"\\otimes":[81],"(arbitrary":[82],"irrep.).":[83],"Our":[84],"yields":[86],"nonstadard":[87],"deformations":[88],"along":[89],"with":[90,135],"nonlinear":[92],"map":[93],"$h$-Borel":[96],"subalgebra":[97],"corresponding":[100],"classical":[101],"Borel":[102],"subalgebra,":[103],"which":[104],"easily":[107],"extended":[108],"to":[109],"whole":[111],"algebra.":[112],"Following":[113],"this":[114],"approach":[115],"we":[116,146],"explicitly":[117],"construct":[118],"here":[119],"Jordanian":[122,151],"quantum":[123],"(super)algebras":[124,132,152],"$U_h(sl(2)),":[125],"U_h(sl(3)),":[126],"U_h(osp(1|2))$":[127],"$U_h(sl(2|1))$.":[129],"These":[130],"Hopf":[131],"equipped":[134],"remarkably":[137],"simpler":[138],"coalgebraic":[139],"structure.":[140],"Generalizing":[141],"results":[143],"$U_h(sl(3))$,":[145],"give":[147],"higher":[149],"dimensional":[150],"$U_h(sl(N))$":[153],"$N$.":[156],"universal":[158],"$R_h$":[159],"also":[162],"given.":[163]},"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}