{"id":"https://openalex.org/W1997444728","doi":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","title":"Crossed Products and Inner Actions of Hopf Algebras","display_name":"Crossed Products and Inner Actions of Hopf Algebras","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W1997444728","doi":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","mag":"1997444728"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1986-0860387-x","doi":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1986-298-02/S0002-9947-1986-0860387-X/S0002-9947-1986-0860387-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084530729","display_name":"Robert J. Blattner","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert J. Blattner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101661101","display_name":"Miriam Cohen","orcid":"https://orcid.org/0000-0003-4953-8701","observed_orcids":["https://orcid.org/0000-0003-4953-8701"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miriam Cohen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108186793","display_name":"Susan Montgomery","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susan Montgomery","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":9.3613,"has_fulltext":false,"cited_by_count":246,"citation_normalized_percentile":{"value":0.9859944,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"298","issue":"2","first_page":"671","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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":1.0,"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":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.0,"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/crossed-products","display_name":"crossed products","score":0.9309999942779541},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.9610000252723694},{"id":"https://openalex.org/keywords/inner-automorphisms","display_name":"inner automorphisms","score":0.8119999766349792},{"id":"https://openalex.org/keywords/derivations","display_name":"derivations","score":0.9470000267028809},{"id":"https://openalex.org/keywords/twisted-products","display_name":"twisted products","score":0.828000009059906},{"id":"https://openalex.org/keywords/semisimple-hopf-algebras","display_name":"semisimple Hopf algebras","score":0.9800000190734863},{"id":"https://openalex.org/keywords/semiprime-algebras","display_name":"semiprime algebras","score":0.8899999856948853},{"id":"https://openalex.org/keywords/noncommutative-algebras","display_name":"noncommutative algebras","score":0.902999997138977}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5984925627708435},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39822542667388916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3977430760860443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3384898006916046}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9947-1986-0860387-x","doi":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1986-0860387-x","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2000643","doi":"https://doi.org/10.2307/2000643","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2000643","pdf_url":"https://www.ams.org/tran/1986-298-02/S0002-9947-1986-0860387-X/S0002-9947-1986-0860387-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2307/2000643","doi":"https://doi.org/10.2307/2000643","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2000643","pdf_url":"https://www.ams.org/tran/1986-298-02/S0002-9947-1986-0860387-X/S0002-9947-1986-0860387-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3452394153","display_name":"Mathematical Sciences: Group Actions on Rings","funder_award_id":"8500959","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997444728.pdf","grobid_xml":"https://content.openalex.org/works/W1997444728.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W145423441","https://openalex.org/W1557525489","https://openalex.org/W1557857086","https://openalex.org/W1976305613","https://openalex.org/W1985068722","https://openalex.org/W1988369858","https://openalex.org/W1989611127","https://openalex.org/W1992429350","https://openalex.org/W1996493357","https://openalex.org/W1998749390","https://openalex.org/W2016319756","https://openalex.org/W2016903768","https://openalex.org/W2017620440","https://openalex.org/W2050236291","https://openalex.org/W2059198995","https://openalex.org/W2061649398","https://openalex.org/W2064777026","https://openalex.org/W2071997637","https://openalex.org/W2077000735","https://openalex.org/W2084069609","https://openalex.org/W2331530531","https://openalex.org/W2594961821","https://openalex.org/W4246894044"],"related_works":["https://openalex.org/W2088257245","https://openalex.org/W2068454011","https://openalex.org/W1606916782","https://openalex.org/W2092420523","https://openalex.org/W2406217023","https://openalex.org/W2129209981","https://openalex.org/W2045609736","https://openalex.org/W2038598420","https://openalex.org/W1996493357","https://openalex.org/W2089756302"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"a":[3,53,61,73,106,118],"theory":[4,20],"of":[5,12,25,41,76,84,130,134,147],"crossed":[6,74,88],"products":[7],"and":[8,28,30],"inner":[9,26,96],"(weak)":[10,145],"actions":[11],"arbitrary":[13],"Hopf":[14,54,81,122],"algebras":[15],"on":[16,97],"noncommutative":[17],"algebras.":[18,42],"The":[19],"covers":[21],"the":[22,79,144],"usual":[23],"examples":[24],"automorphisms":[27],"derivations,":[29],"in":[31,138],"addition":[32],"is":[33,52,58,66,103,117,141,149],"general":[34],"enough":[35],"to":[36,69,105],"include":[37],"\"inner\"":[38],"group":[39],"gradings":[40],"We":[43],"prove":[44],"that":[45,133],"if":[46,115,143],"$\\pi":[47],":H":[48],"\\to":[49],"\\overline":[50],"H$":[51],"algebra":[55,67],"epimorphism":[56],"which":[57],"split":[59],"as":[60],"coalgebra":[62],"map,":[63],"then":[64,99],"$H$":[65,77,94,116,148],"isomorphic":[68,104],"$A{\\#":[70,90,100,135],"_\\sigma":[71,91,101,136],"}H$,":[72],"product":[75,89,108],"with":[78,93,111],"left":[80],"kernel":[82],"$A$":[83,131],"$\\pi$.":[85],"Given":[86],"any":[87],"}H$":[92,102],"(weakly)":[95],"$A$,":[98],"twisted":[107],"${A_\\tau":[109],"}[H]$":[110],"trivial":[112],"action.":[113],"Finally,":[114],"finite":[119],"dimensional":[120],"semisimple":[121],"algebra,":[123],"we":[124],"consider":[125],"when":[126],"semisimplicity":[127],"or":[128],"semiprimeness":[129],"implies":[132],"}H$;":[137],"particular":[139],"this":[140],"true":[142],"action":[146],"inner.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}