{"id":"https://openalex.org/W7204168613","doi":"https://doi.org/10.48550/arxiv.2608.22195","title":"Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions","display_name":"Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions","publication_year":2026,"publication_date":"2026-08-23","ids":{"openalex":"https://openalex.org/W7204168613","doi":"https://doi.org/10.48550/arxiv.2608.22195"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.22195","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22195","pdf_url":"https://arxiv.org/pdf/2608.22195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.22195","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017970856","display_name":"Daowei Lu","orcid":"https://orcid.org/0000-0002-8256-8745","observed_orcids":["https://orcid.org/0000-0002-8256-8745"]},"institutions":[{"id":"https://openalex.org/I4210127530","display_name":"Jining University","ror":"https://ror.org/037rvh518","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu, Daowei","raw_affiliation_strings":["School of Mathematics and Big Data , Jining University Qufu , Shandong 273155 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data , Jining University Qufu , Shandong 273155 , P. R. China","institution_ids":["https://openalex.org/I4210127530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148058329","display_name":"Dingguo Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]},{"id":"https://openalex.org/I4210103733","display_name":"Shandong Xiehe University","ror":"https://ror.org/01bx4e159","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210103733"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Dingguo","raw_affiliation_strings":["Department of General Education , Shandong Xiehe University Jinan , Shandong , 250109 , P. R. China","School of Mathematical Sciences , Qufu Normal University Qufu , Shandong 273165 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of General Education , Shandong Xiehe University Jinan , Shandong , 250109 , P. R. China","institution_ids":["https://openalex.org/I4210103733"]},{"raw_affiliation_string":"School of Mathematical Sciences , Qufu Normal University Qufu , Shandong 273165 , P. R. China","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9657999873161316,"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":0.9657999873161316,"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":0.012299999594688416,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.008999999612569809,"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/hochschild-cohomology","display_name":"Hochschild cohomology","score":0.9480000138282776},{"id":"https://openalex.org/keywords/weak-hopf-algebras","display_name":"weak Hopf algebras","score":0.9559999704360962},{"id":"https://openalex.org/keywords/bijective-antipode","display_name":"bijective antipode","score":0.7680000066757202},{"id":"https://openalex.org/keywords/spectral-sequences","display_name":"spectral sequences","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7910000085830688},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6478000283241272},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.6104999780654907},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5827999711036682},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5392000079154968},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31769999861717224},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26440000534057617}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.22195","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22195","pdf_url":"https://arxiv.org/pdf/2608.22195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.22195","doi":"https://doi.org/10.48550/arxiv.2608.22195","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.22195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.22195","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22195","pdf_url":"https://arxiv.org/pdf/2608.22195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4636551430","display_name":null,"funder_award_id":"11901240","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8503811393","display_name":null,"funder_award_id":"12271292","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204168613.pdf","grobid_xml":"https://content.openalex.org/works/W7204168613.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415816717","https://openalex.org/W2261678548","https://openalex.org/W2065385225","https://openalex.org/W2936092116","https://openalex.org/W2963761400","https://openalex.org/W2387468014","https://openalex.org/W2058444534","https://openalex.org/W2298804496","https://openalex.org/W4405095620","https://openalex.org/W1976140352"],"abstract_inverted_index":{"Let":[0],"$H$":[1],"be":[2],"a":[3,59],"weak":[4,22,34],"Hopf":[5],"algebra":[6,63],"with":[7],"bijective":[8],"antipode.":[9],"This":[10],"paper":[11],"is":[12,58,66],"devoted":[13],"to":[14],"the":[15,31,40,44,70],"AS-Gorenstein":[16,71],"property":[17],"of":[18,28,33,47,50],"restricted":[19],"faithfully":[20],"flat":[21],"$H$-Galois":[23,35],"extensions":[24,36],"$A/B$.":[25],"We":[26],"first":[27],"all":[29],"study":[30],"cohomologies":[32,46],"and":[37,49,64],"then":[38],"establish":[39],"spectral":[41],"sequence":[42],"connecting":[43],"Hochschild":[45],"$A$":[48,57,68],"$B$.":[51],"Finally":[52],"we":[53],"prove":[54],"that":[55],"when":[56],"noetherian":[60],"affine":[61],"PI":[62],"$B$":[65],"AS-Gorenstein,":[67],"shares":[69],"property.":[72]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-26T00:00:00"}