{"id":"https://openalex.org/W7213595675","doi":"https://doi.org/10.48550/arxiv.2609.19560","title":"Gerstenhaber algebra structure on the Hochschild cohomology ring of the Xu--Snashall algebra","display_name":"Gerstenhaber algebra structure on the Hochschild cohomology ring of the Xu--Snashall algebra","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213595675","doi":"https://doi.org/10.48550/arxiv.2609.19560"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19560","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19560","pdf_url":"https://arxiv.org/pdf/2609.19560","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.19560","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152119077","display_name":"Qi Long","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long, Qi","raw_affiliation_strings":["Normal University Shanghai 200241 , P. R. China","PMMP , East China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normal University Shanghai 200241 , P. R. China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"PMMP , East China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134621404","display_name":"Ziyang Shi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi, Ziyang","raw_affiliation_strings":["Normal University Shanghai 200241 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normal University Shanghai 200241 , P. R. China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045549126","display_name":"Guodong Zhou","orcid":"https://orcid.org/0000-0002-3658-9967","observed_orcids":["https://orcid.org/0000-0002-3658-9967"]},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Guodong","raw_affiliation_strings":["Normal University Shanghai 200241 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Normal University Shanghai 200241 , P. R. China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21945476"],"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":0.5551999807357788,"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":0.5551999807357788,"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":0.41530001163482666,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.007400000002235174,"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/gerstenhaber-algebras","display_name":"Gerstenhaber algebras","score":0.8949999809265137},{"id":"https://openalex.org/keywords/hochschild-cohomology-ring","display_name":"Hochschild cohomology ring","score":0.9789999723434448},{"id":"https://openalex.org/keywords/finite-dimensional-algebras","display_name":"finite-dimensional algebras","score":0.8690000176429749},{"id":"https://openalex.org/keywords/nilpotent-elements","display_name":"nilpotent elements","score":0.7770000100135803},{"id":"https://openalex.org/keywords/finitely-generated-algebras","display_name":"finitely generated algebras","score":0.8550000190734863},{"id":"https://openalex.org/keywords/support-varieties","display_name":"support varieties","score":0.8209999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7437000274658203},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6140000224113464},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5795000195503235},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.501800000667572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4875999987125397},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.47699999809265137},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.40070000290870667},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.3066999912261963},{"id":"https://openalex.org/C2777041388","wikidata":"https://www.wikidata.org/wiki/Q6664297","display_name":"Local cohomology","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.28119999170303345},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C2776456406","wikidata":"https://www.wikidata.org/wiki/Q6664692","display_name":"Locally nilpotent","level":4,"score":0.2680000066757202},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19560","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19560","pdf_url":"https://arxiv.org/pdf/2609.19560","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.2609.19560","doi":"https://doi.org/10.48550/arxiv.2609.19560","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19560","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.19560","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19560","pdf_url":"https://arxiv.org/pdf/2609.19560","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213595675.pdf","grobid_xml":"https://content.openalex.org/works/W7213595675.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7203769454","https://openalex.org/W2359538216","https://openalex.org/W2971670814","https://openalex.org/W3014860045","https://openalex.org/W2040928331","https://openalex.org/W2156810290","https://openalex.org/W1968554611","https://openalex.org/W1972470703","https://openalex.org/W7095883354","https://openalex.org/W2017773539"],"abstract_inverted_index":{"Let":[0],"$A$":[1],"be":[2,10],"a":[3,17,57,63,70,90,134,150,158],"finite":[4,151],"dimensional":[5,152],"algebra":[6,93,119,153],"and":[7,51,76,94,169],"let":[8],"$\\rmHH^*(A)$":[9],"its":[11],"Hochschild":[12,48,123],"cohomology":[13,124],"ring,":[14,125],"which":[15],"is":[16,56,89,132,156],"Gerstenhaber":[18,30,32,118],"algebra.":[19,60,100,111,137,161],"Denote":[20],"by":[21,35,41,114],"$\\calN$":[22],"(resp.":[23,28],"$G$,":[24],"$\\calG$)":[25],"the":[26,66,98,109,117,122],"ideal":[27],"weak":[29,170],"ideal,":[31],"ideal)":[33],"generated":[34,59,92,136,160],"all":[36],"homogeneous":[37],"nilpotent":[38],"elements.":[39],"Motivated":[40],"their":[42],"work":[43],"on":[44,121],"support":[45],"varieties":[46],"via":[47],"cohomology,":[49],"Snashall":[50,77],"Solberg":[52],"conjectured":[53],"that":[54,128,141],"$\\rmHH^*(A)/\\calN$":[55],"finitely":[58,91,135,159],"Xu":[61],"constructed":[62],"counterexample":[64],"to":[65,81],"Snashall-Solberg":[67],"conjecture":[68],"over":[69],"base":[71],"field":[72],"of":[73],"characteristic":[74],"two,":[75],"generalized":[78],"this":[79,102,106],"example":[80],"arbitrary":[82],"characteristic.":[83],"Hermann":[84],"further":[85],"asked":[86],"whether":[87],"$\\rmHH^*(A)/G$":[88],"suggested":[95],"considering":[96],"first":[97],"Xu--Snashall":[99,110],"In":[101,112],"paper,":[103],"we":[104,126,139],"answer":[105],"question":[107],"for":[108,149],"fact,":[113],"explicitly":[115],"computing":[116],"structure":[120],"show":[127,140],"$G=\\calN$;":[129],"hence":[130],"$\\rmHH^*(A)/G=\\rmHH^*(A)/\\calN$":[131],"not":[133],"Furthermore,":[138],"$\\rmHH^*(A)/\\calG\\cong":[142],"K$.":[143],"Therefore,":[144],"one":[145],"may":[146],"ask":[147],"whether,":[148],"$A$,":[154],"$\\rmHH^*(A)/\\calG$":[155],"always":[157],"Our":[162],"main":[163],"tools":[164],"are":[165],"two-sided":[166],"Anick":[167],"resolutions":[168],"self-homotopies.":[171]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-19T00:00:00"}