{"id":"https://openalex.org/W1968086157","doi":"https://doi.org/10.1142/s0218196791000134","title":"HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS","display_name":"HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS","publication_year":1991,"publication_date":"1991-06-01","ids":{"openalex":"https://openalex.org/W1968086157","doi":"https://doi.org/10.1142/s0218196791000134","mag":"1968086157"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196791000134","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196791000134","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085392129","display_name":"Jean\u2010Yves Thibon","orcid":"https://orcid.org/0000-0002-8976-4044"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210116548","display_name":"Laboratoire de Statistique Th\u00e9orique et Appliqu\u00e9e","ror":"https://ror.org/01vnn4t89","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210116548","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"JEAN-YVES THIBON","raw_affiliation_strings":["Laboratoire d'Informatique Th\u00e9orique et Programmation, Universit\u00e9 Paris 7, 2, place Jussieu, 75251 Paris Cedex 05, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Th\u00e9orique et Programmation, Universit\u00e9 Paris 7, 2, place Jussieu, 75251 Paris Cedex 05, France","institution_ids":["https://openalex.org/I4210116548","https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085392129"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210116548"],"apc_list":null,"apc_paid":null,"fwci":2.1289,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.8439138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"01","issue":"02","first_page":"207","last_page":"221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9973999857902527,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.8883556127548218},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.7855387926101685},{"id":"https://openalex.org/keywords/tensor-product-of-hilbert-spaces","display_name":"Tensor product of Hilbert spaces","score":0.6773748397827148},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6704005002975464},{"id":"https://openalex.org/keywords/tensor-product-of-algebras","display_name":"Tensor product of algebras","score":0.666741132736206},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6026134490966797},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.5889692306518555},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5554599761962891},{"id":"https://openalex.org/keywords/ring-of-symmetric-functions","display_name":"Ring of symmetric functions","score":0.551565945148468},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5463488698005676},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.533494770526886},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4975948631763458},{"id":"https://openalex.org/keywords/quantum-group","display_name":"Quantum group","score":0.49020200967788696},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.47527188062667847},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.47234833240509033},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.4649101197719574},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4294387102127075},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.41461318731307983},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.16780343651771545},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12522190809249878},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0820637047290802}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8883556127548218},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.7855387926101685},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.6773748397827148},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6704005002975464},{"id":"https://openalex.org/C41678559","wikidata":"https://www.wikidata.org/wiki/Q7700713","display_name":"Tensor product of algebras","level":5,"score":0.666741132736206},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6026134490966797},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.5889692306518555},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5554599761962891},{"id":"https://openalex.org/C156903151","wikidata":"https://www.wikidata.org/wiki/Q17102788","display_name":"Ring of symmetric functions","level":4,"score":0.551565945148468},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5463488698005676},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.533494770526886},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4975948631763458},{"id":"https://openalex.org/C148647251","wikidata":"https://www.wikidata.org/wiki/Q2122223","display_name":"Quantum group","level":3,"score":0.49020200967788696},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47527188062667847},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.47234833240509033},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.4649101197719574},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4294387102127075},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.41461318731307983},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.16780343651771545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12522190809249878},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0820637047290802},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196791000134","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196791000134","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2041404781","https://openalex.org/W2949343535","https://openalex.org/W4298347446","https://openalex.org/W2186765725","https://openalex.org/W2948436065","https://openalex.org/W1981526234","https://openalex.org/W2619660439","https://openalex.org/W3036032705","https://openalex.org/W4382618720","https://openalex.org/W3134691306"],"abstract_inverted_index":{"The":[0],"Hopf":[1],"algebra":[2],"structure":[3],"of":[4,7,29,51,59],"the":[5,18,22,26,44],"ring":[6],"symmetric":[8,30],"functions":[9],"is":[10],"used":[11],"to":[12,25],"prove":[13],"a":[14],"new":[15],"identity":[16],"for":[17],"internal":[19],"product,":[20],"i.e.,":[21],"operation":[23],"corresponding":[24],"tensor":[27],"product":[28],"group":[31],"representations.":[32],"From":[33],"this":[34,56],"identity,":[35],"or":[36],"by":[37],"similar":[38],"techniques":[39],"which":[40],"can":[41],"also":[42],"involve":[43],"\u03bb-ring":[45],"structure,":[46],"we":[47],"derive":[48],"easy":[49],"proofs":[50],"most":[52],"known":[53],"results":[54,61],"about":[55],"operation.":[57],"Some":[58],"these":[60],"are":[62],"generalized.":[63]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
