{"id":"https://openalex.org/W4416451663","doi":"https://doi.org/10.1142/s0219199726500070","title":"Burnside-type results for fusion categories","display_name":"Burnside-type results for fusion categories","publication_year":2025,"publication_date":"2025-11-21","ids":{"openalex":"https://openalex.org/W4416451663","doi":"https://doi.org/10.1142/s0219199726500070"},"language":"en","primary_location":{"id":"doi:10.1142/s0219199726500070","doi":"https://doi.org/10.1142/s0219199726500070","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219199726500070","pdf_url":null,"source":{"id":"https://openalex.org/S51811661","display_name":"Communications in Contemporary Mathematics","issn_l":"0219-1997","issn":["0219-1997","1793-6683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-140","russia-white-list-1"],"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":"Communications in Contemporary Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2302.07604","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068935307","display_name":"Sebastian Burciu","orcid":"https://orcid.org/0000-0001-7016-5749","observed_orcids":["https://orcid.org/0000-0001-7016-5749"]},"institutions":[{"id":"https://openalex.org/I4405262991","display_name":"IMAR - Institutul de Matematic\u0103 \u201eSimion Stoilow\u201d al Academiei Rom\u00e2ne","ror":"https://ror.org/0122mh736","country_code":"RO","type":"education","lineage":["https://openalex.org/I4405262991","https://openalex.org/I58077936"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Sebastian Burciu","raw_affiliation_strings":["Institute of Mathematics \u201cSimion Stoilow\u201d of the Romanian Academy, P.O. Box 1-764, Bucharest RO-014700, Romania"],"raw_orcid":"https://orcid.org/0000-0001-7016-5749","affiliations":[{"raw_affiliation_string":"Institute of Mathematics \u201cSimion Stoilow\u201d of the Romanian Academy, P.O. Box 1-764, Bucharest RO-014700, Romania","institution_ids":["https://openalex.org/I4405262991","https://openalex.org/I58077936"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071902780","display_name":"S\u00e9bastien Palcoux","orcid":"https://orcid.org/0000-0002-0244-302X","observed_orcids":["https://orcid.org/0000-0002-0244-302X"]},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":null,"type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sebastien Palcoux","raw_affiliation_strings":["Beijing Institute of Mathematical Sciences and Applications, Huairou District, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-0244-302X","affiliations":[{"raw_affiliation_string":"Beijing Institute of Mathematical Sciences and Applications, Huairou District, Beijing, China","institution_ids":["https://openalex.org/I4403928416"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7615,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86608069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"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":0.9340999722480774,"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":0.9340999722480774,"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/T10849","display_name":"Finite Group Theory Research","score":0.039900001138448715,"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":0.004600000102072954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/burnside-s-theorem","display_name":"Burnside's theorem","score":0.9079999923706055},{"id":"https://openalex.org/keywords/fusion-categories","display_name":"fusion categories","score":0.7789999842643738},{"id":"https://openalex.org/keywords/character-tables","display_name":"character tables","score":0.7210000157356262},{"id":"https://openalex.org/keywords/grothendieck-ring","display_name":"Grothendieck ring","score":0.9340000152587891}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8450000286102295},{"id":"https://openalex.org/C1219285","wikidata":"https://www.wikidata.org/wiki/Q5051825","display_name":"Categorification","level":2,"score":0.7960000038146973},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5767999887466431},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.5491999983787537},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.5278000235557556},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4406999945640564},{"id":"https://openalex.org/C2778971668","wikidata":"https://www.wikidata.org/wiki/Q5510284","display_name":"Fusion rules","level":4,"score":0.4359000027179718},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3138999938964844},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.30570000410079956},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.29660001397132874},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.289900004863739},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C122022638","wikidata":"https://www.wikidata.org/wiki/Q1128678","display_name":"Grothendieck group","level":3,"score":0.27459999918937683}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219199726500070","doi":"https://doi.org/10.1142/s0219199726500070","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219199726500070","pdf_url":null,"source":{"id":"https://openalex.org/S51811661","display_name":"Communications in Contemporary Mathematics","issn_l":"0219-1997","issn":["0219-1997","1793-6683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-140","russia-white-list-1"],"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":"Communications in Contemporary Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2302.07604","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.07604","pdf_url":"https://arxiv.org/pdf/2302.07604","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.2302.07604","doi":"https://doi.org/10.48550/arxiv.2302.07604","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2302.07604","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2302.07604","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.07604","pdf_url":"https://arxiv.org/pdf/2302.07604","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6807771780","display_name":null,"funder_award_id":"PN-III-P4-ID-PCE- 2020-0878","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"},{"id":"https://openalex.org/G7653980947","display_name":null,"funder_award_id":"12471031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8036046488","display_name":null,"funder_award_id":"PN-III-P4-ID-PCE-2020-0878","funder_id":"https://openalex.org/F4320318622","funder_display_name":"Ministerul Cercet\u0103rii, Inov\u0103rii \u015fi Digitaliz\u0103rii"}],"funders":[{"id":"https://openalex.org/F4320318622","display_name":"Ministerul Cercet\u0103rii, Inov\u0103rii \u015fi Digitaliz\u0103rii","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323983","display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","ror":"https://ror.org/01q7jq182"},{"id":"https://openalex.org/F4320336189","display_name":"Colegiul Consultativ pentru Cercetare-Dezvoltare \u015fi Inovare","ror":"https://ror.org/03mc0m715"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416451663.pdf","grobid_xml":"https://content.openalex.org/works/W4416451663.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,103],"this":[1],"paper,":[2],"we":[3,62,79,105],"extend":[4],"a":[5,30,168,191],"classical":[6],"vanishing":[7,42],"result":[8],"of":[9,15,22,33,68,89,118,139,173],"Burnside":[10],"from":[11],"the":[12,19,40,65,86,95,113],"character":[13,20],"tables":[14,21],"finite":[16],"groups":[17],"to":[18,29],"commutative":[23],"fusion":[24,50,72,92,122,137,171,188],"rings,":[25],"or":[26],"more":[27],"generally":[28],"certain":[31],"class":[32],"abelian":[34],"normalizable":[35],"hypergroups.":[36],"We":[37,44,180],"also":[38,181],"treat":[39],"dual":[41],"result.":[43],"show":[45],"that":[46,64,83],"any":[47,69,90],"nilpotent":[48],"unitary":[49],"categories":[51],"satisfy":[52],"both":[53,75],"Burnside\u2019s":[54],"property":[55],"and":[56,109,116,156],"its":[57],"dual.":[58],"Using":[59],"Drinfeld\u2019s":[60],"map,":[61],"obtain":[63],"Grothendieck":[66,87],"ring":[67,88],"weakly-integral":[70,91],"modular":[71,136,170,187],"category":[73,93,138],"satisfies":[74],"properties.":[76],"As":[77],"applications,":[78],"prove":[80],"new":[81,100,183],"identities":[82],"hold":[84],"in":[85],"satisfying":[94],"dual-Burnside\u2019s":[96],"property,":[97],"thus":[98],"providing":[99],"categorification":[101],"criteria.":[102],"particular,":[104],"improve":[106],"[V.":[107],"Ostrik":[108],"Z.":[110],"Yu,":[111],"On":[112],"minimal":[114],"extension":[115],"structure":[117],"braided":[119],"weakly":[120,134],"group-theoretical":[121],"categories,":[123,189],"Adv.":[124],"Math.":[125],"419":[126],"(2023)":[127],"108961,":[128],"Theorem":[129],"4.5]":[130],"as":[131],"follows:":[132],"A":[133],"integral":[135],"[Formula:":[140,143,147,153,157,164,174,177],"see":[141,144,148,154,158,165,175,178],"text]":[142,145,149,155,159,176],"with":[146,152],"square-free":[150],"coprime":[151],"for":[160],"every":[161],"simple":[162],"object":[163],"text],":[166],"has":[167],"pointed":[169],"subcategory":[172],"text].":[179],"present":[182],"results":[184],"on":[185],"perfect":[186],"including":[190],"Cauchy-type":[192],"theorem.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2025-11-23T00:00:00"}
