{"id":"https://openalex.org/W4392575236","doi":"https://doi.org/10.48550/arxiv.2403.02643","title":"Constructing Modular Tensor Categories with Hopf Algebras","display_name":"Constructing Modular Tensor Categories with Hopf Algebras","publication_year":2024,"publication_date":"2024-03-05","ids":{"openalex":"https://openalex.org/W4392575236","doi":"https://doi.org/10.48550/arxiv.2403.02643"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2403.02643","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.02643","pdf_url":"https://arxiv.org/pdf/2403.02643","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.02643","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhou, Kun","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhou, Kun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9067000150680542,"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":0.9067000150680542,"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":0.0868000015616417,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.000699999975040555,"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/modular-tensor-categories","display_name":"modular tensor categories","score":1.0},{"id":"https://openalex.org/keywords/pointed-hopf-algebras","display_name":"pointed Hopf algebras","score":0.8679999709129333},{"id":"https://openalex.org/keywords/representation-categories","display_name":"representation categories","score":0.640999972820282},{"id":"https://openalex.org/keywords/drinfeld-double","display_name":"Drinfeld double","score":0.8489999771118164},{"id":"https://openalex.org/keywords/quantum-groups","display_name":"quantum groups","score":0.6460000276565552},{"id":"https://openalex.org/keywords/semisimple-hopf-algebras","display_name":"semisimple Hopf algebras","score":0.777999997138977}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6942383050918579},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6757915019989014},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6346370577812195},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48622193932533264},{"id":"https://openalex.org/C41678559","wikidata":"https://www.wikidata.org/wiki/Q7700713","display_name":"Tensor product of algebras","level":5,"score":0.4746055006980896},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4584819972515106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.447549432516098},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3622411787509918},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.35928115248680115},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.3246912956237793},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.2889467477798462},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16001349687576294}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2403.02643","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.02643","pdf_url":"https://arxiv.org/pdf/2403.02643","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.2403.02643","doi":"https://doi.org/10.48550/arxiv.2403.02643","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2403.02643","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:2403.02643","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.02643","pdf_url":"https://arxiv.org/pdf/2403.02643","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392575236.pdf","grobid_xml":"https://content.openalex.org/works/W4392575236.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W132488082","https://openalex.org/W2171365950","https://openalex.org/W2318184750","https://openalex.org/W2496100290","https://openalex.org/W4297845514","https://openalex.org/W2469343812","https://openalex.org/W2058488146","https://openalex.org/W2810638431","https://openalex.org/W2606548108","https://openalex.org/W2068945702"],"abstract_inverted_index":{"A":[0],"modular":[1,27,42,119,160],"tensor":[2,9,28,120,125,161,177],"category":[3],"is":[4,17,35],"a":[5,12,26,61,67,73,81,137],"non-degenerate":[6],"ribbon":[7,13,78,101,141],"finite":[8,87],"category.":[10,29],"And":[11,154],"factorizable":[14,68,102,142],"Hopf":[15,20,45,54,63,90,103,143,181],"algebra":[16,21,64],"exactly":[18],"the":[19],"whose":[22],"finite-dimensional":[23],"representations":[24],"form":[25],"The":[30],"goal":[31],"of":[32,53,100,130,139,179],"this":[33],"paper":[34],"to":[36,65,76,85,108,127],"construct":[37,136],"both":[38],"semisimple":[39,140],"and":[40,56,96,163,188],"non-semisimple":[41],"categories":[43,116,121,129,162],"with":[44],"algebras.":[46,104],"In":[47],"particular,":[48],"we":[49,71,83,111,135,155],"study":[50],"central":[51],"extensions":[52],"algebras":[55,91,182,184],"characterize":[57],"some":[58,86,152,171],"conditions":[59],"for":[60],"quotient":[62],"be":[66,168],"one.":[69],"Then":[70],"give":[72],"special":[74],"way":[75],"obtain":[77,97],"elements.":[79],"As":[80],"result,":[82],"apply":[84],"dimensional":[88],"pointed":[89],"introduced":[92],"by":[93,170],"Andruskiewitsch":[94],"etc":[95],"two":[98],"families":[99],"With":[105],"little":[106],"restrictions":[107],"their":[109,114,186],"parameters,":[110],"prove":[112,164],"that":[113,165],"representation":[115,128],"are":[117,123,148],"prime":[118,149,159],"which":[122],"not":[124,176],"equivalent":[126],"small":[131],"quantum":[132],"groups.":[133],"Lastly,":[134],"family":[138],"algebas":[144],"A(p,q),":[145],"where":[146],"p,q":[147],"numbers":[150],"satisfying":[151],"conditions.":[153],"decompose":[156],"Rep(A(p,q))":[157],"into":[158],"A(p,q)":[166],"can't":[167],"obtained":[169],"obvious":[172],"ways,":[173],"i.e.":[174],"it's":[175],"product":[178],"trivial":[180],"(group":[183],"or":[185],"dual)":[187],"Drinfeld":[189],"doubles.":[190]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}