{"id":"https://openalex.org/W2084433752","doi":"https://doi.org/10.1017/s0017089512000808","title":"GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS","display_name":"GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS","publication_year":2013,"publication_date":"2013-02-25","ids":{"openalex":"https://openalex.org/W2084433752","doi":"https://doi.org/10.1017/s0017089512000808","mag":"2084433752"},"language":"en","primary_location":{"id":"doi:10.1017/s0017089512000808","doi":"https://doi.org/10.1017/s0017089512000808","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0017089512000808","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9DCF3EE52D7168CC7C37DFECE159A679/S0017089512000808a.pdf/div-class-title-group-bialgebras-and-permutation-bialgebras-div.pdf","source":{"id":"https://openalex.org/S190308653","display_name":"Glasgow Mathematical Journal","issn_l":"0017-0895","issn":["0017-0895","1469-509X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Glasgow Mathematical Journal","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9DCF3EE52D7168CC7C37DFECE159A679/S0017089512000808a.pdf/div-class-title-group-bialgebras-and-permutation-bialgebras-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037127869","display_name":"Martin D. Crossley","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"MARTIN CROSSLEY","raw_affiliation_strings":["Department of Mathematics, Swansea University, Swansea SA2 8PP, Wales e-mail:","Department of Mathematics, Swansea University, Swansea SA2 8PP, Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Swansea University, Swansea SA2 8PP, Wales e-mail:","institution_ids":["https://openalex.org/I39586589"]},{"raw_affiliation_string":"Department of Mathematics, Swansea University, Swansea SA2 8PP, Wales","institution_ids":["https://openalex.org/I39586589"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037127869"],"corresponding_institution_ids":["https://openalex.org/I39586589"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15001982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"3","first_page":"639","last_page":"643"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5009999871253967,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5009999871253967,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.4887999892234802,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.004100000020116568,"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/symmetric-group","display_name":"symmetric group","score":0.6359999775886536},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.8989999890327454},{"id":"https://openalex.org/keywords/convolution-product","display_name":"convolution product","score":0.6800000071525574},{"id":"https://openalex.org/keywords/zero-divisors","display_name":"zero divisors","score":0.628000020980835}],"concepts":[{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.8455435633659363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8432797789573669},{"id":"https://openalex.org/C130856480","wikidata":"https://www.wikidata.org/wiki/Q7269541","display_name":"Quasitriangular Hopf algebra","level":5,"score":0.6394221186637878},{"id":"https://openalex.org/C2778676360","wikidata":"https://www.wikidata.org/wiki/Q494141","display_name":"Bialgebra","level":4,"score":0.6279507875442505},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.6091300249099731},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5884734392166138},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5132708549499512},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5122829675674438},{"id":"https://openalex.org/C55192134","wikidata":"https://www.wikidata.org/wiki/Q7314221","display_name":"Representation theory of Hopf algebras","level":5,"score":0.47869446873664856},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4646816551685333},{"id":"https://openalex.org/C120047569","wikidata":"https://www.wikidata.org/wiki/Q92795049","display_name":"Group algebra","level":3,"score":0.46233034133911133},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4422285556793213},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.429246187210083},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42840132117271423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4221344590187073},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4131513237953186},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.4036068022251129},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.27396708726882935},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0017089512000808","doi":"https://doi.org/10.1017/s0017089512000808","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0017089512000808","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9DCF3EE52D7168CC7C37DFECE159A679/S0017089512000808a.pdf/div-class-title-group-bialgebras-and-permutation-bialgebras-div.pdf","source":{"id":"https://openalex.org/S190308653","display_name":"Glasgow Mathematical Journal","issn_l":"0017-0895","issn":["0017-0895","1469-509X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Glasgow Mathematical Journal","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0017089512000808","doi":"https://doi.org/10.1017/s0017089512000808","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0017089512000808","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9DCF3EE52D7168CC7C37DFECE159A679/S0017089512000808a.pdf/div-class-title-group-bialgebras-and-permutation-bialgebras-div.pdf","source":{"id":"https://openalex.org/S190308653","display_name":"Glasgow Mathematical Journal","issn_l":"0017-0895","issn":["0017-0895","1469-509X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Glasgow Mathematical Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084433752.pdf","grobid_xml":"https://content.openalex.org/works/W2084433752.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W93573449","https://openalex.org/W2010073471","https://openalex.org/W2094508920","https://openalex.org/W4205256130"],"related_works":["https://openalex.org/W2496922404","https://openalex.org/W2043574034","https://openalex.org/W1704428419","https://openalex.org/W7095710070","https://openalex.org/W4212851075","https://openalex.org/W7096284364","https://openalex.org/W1995804643","https://openalex.org/W2148474862","https://openalex.org/W7099228933","https://openalex.org/W1524905548"],"abstract_inverted_index":{"Abstract":[0],"Malvenuto":[1,5],"and":[2,6,13,89,113],"Reutenauer":[3],"(C.":[4],"C.":[7],"Reutenauer,":[8],"Duality":[9],"between":[10],"quasi-symmetric":[11],"functions":[12],"the":[14,24,44,57,69,86,93,128,131,143,146],"Solomon":[15,45],"descent":[16,46,156],"algebra,":[17],"J.":[18],"Algebra177":[19],"(1995),":[20],"967\u2013982)":[21],"showed":[22],"how":[23],"total":[25],"symmetric":[26,132],"group":[27,58,70,87,125],"ring":[28],"\u2295nZ\u03a3n":[29],"could":[30],"be":[31,118,159],"made":[32],"into":[33],"a":[34,38,49,61,104],"Hopf":[35,105],"algebra":[36,47,106],"with":[37],"very":[39],"nice":[40],"structure":[41,67,71,107],"which":[42,154],"admitted":[43],"as":[48],"sub-Hopf":[50],"algebra.":[51],"To":[52],"do":[53],"this":[54,75],"they":[55],"replaced":[56],"multiplication":[59],"by":[60],"convolution":[62],"product,":[63],"thus":[64],"distancing":[65],"their":[66],"from":[68,121],"of":[72,99,124,130],"\u03a3n.":[73],"In":[74,127],"paper":[76],"we":[77,83,90,134],"examine":[78],"what":[79],"is":[80,108],"possible":[81],"if":[82],"keep":[84],"to":[85],"multiplication,":[88],"also":[91],"consider":[92],"question":[94],"for":[95],"more":[96],"general":[97],"families":[98],"groups.":[100],"We":[101],"show":[102],"that":[103,136,145],"not":[109],"possible,":[110],"but":[111,152],"cocommutative":[112],"non-cocommutative":[114],"counital":[115],"bialgebras":[116],"can":[117,158],"obtained,":[119],"arising":[120],"certain":[122],"diagrams":[123],"homomorphisms.":[126],"case":[129],"groups":[133],"note":[135],"all":[137],"such":[138],"structures":[139,153],"are":[140],"weak":[141],"in":[142],"sense":[144],"dual":[147],"algebras":[148],"have":[149],"many":[150],"zero-divisors,":[151],"respect":[155],"sums":[157],"found.":[160]},"counts_by_year":[],"updated_date":"2026-09-09T07:26:56.047234","created_date":"2016-06-24T00:00:00"}