{"id":"https://openalex.org/W7204886831","doi":"https://doi.org/10.48550/arxiv.2608.29782","title":"Poisson bialgebras by deformations-to-quasiclassical limits","display_name":"Poisson bialgebras by deformations-to-quasiclassical limits","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204886831","doi":"https://doi.org/10.48550/arxiv.2608.29782"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29782","pdf_url":"https://arxiv.org/pdf/2608.29782","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/2608.29782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100429250","display_name":"Siyuan Chen","orcid":"https://orcid.org/0009-0001-8475-0305","observed_orcids":["https://orcid.org/0009-0001-8475-0305"]},"institutions":[{"id":"https://openalex.org/I100286613","display_name":"Hunan Institute of Science and Technology","ror":"https://ror.org/044ysd349","country_code":"CN","type":"education","lineage":["https://openalex.org/I100286613"]},{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Siyuan","raw_affiliation_strings":["Chern Institute of Mathematics & LPMC , Nankai University , Tianjin 300071 China","School of mathematics , Hunan Institute of Science and Technology , Yueyang , Hunan Province 414006 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics & LPMC , Nankai University , Tianjin 300071 China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"School of mathematics , Hunan Institute of Science and Technology , Yueyang , Hunan Province 414006 , China","institution_ids":["https://openalex.org/I100286613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014897749","display_name":"Chengming Bai","orcid":"https://orcid.org/0000-0002-9242-5887","observed_orcids":["https://orcid.org/0000-0002-9242-5887"]},"institutions":[{"id":"https://openalex.org/I100286613","display_name":"Hunan Institute of Science and Technology","ror":"https://ror.org/044ysd349","country_code":"CN","type":"education","lineage":["https://openalex.org/I100286613"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai, Chengming","raw_affiliation_strings":["School of mathematics , Hunan Institute of Science and Technology , Yueyang , Hunan Province 414006 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of mathematics , Hunan Institute of Science and Technology , Yueyang , Hunan Province 414006 , China","institution_ids":["https://openalex.org/I100286613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9976000189781189,"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":0.9976000189781189,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0019000000320374966,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":9.999999747378752e-05,"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/semiclassical-limit","display_name":"semiclassical limit","score":0.9200000166893005},{"id":"https://openalex.org/keywords/manin-triples","display_name":"Manin triples","score":0.8560000061988831},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.9629999995231628}],"concepts":[{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.8865000009536743},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.8464999794960022},{"id":"https://openalex.org/C2778676360","wikidata":"https://www.wikidata.org/wiki/Q494141","display_name":"Bialgebra","level":4,"score":0.7692000269889832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7142000198364258},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6947000026702881},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6482999920845032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5536999702453613},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5479999780654907},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5239999890327454},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C51292594","wikidata":"https://www.wikidata.org/wiki/Q744960","display_name":"Associative algebra","level":5,"score":0.3790000081062317},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.3767000138759613},{"id":"https://openalex.org/C4161247","wikidata":"https://www.wikidata.org/wiki/Q11143305","display_name":"Poisson algebra","level":4,"score":0.36550000309944153},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C2778249326","wikidata":"https://www.wikidata.org/wiki/Q1777803","display_name":"Coalgebra","level":3,"score":0.3361999988555908},{"id":"https://openalex.org/C188845816","wikidata":"https://www.wikidata.org/wiki/Q1052775","display_name":"Poisson bracket","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.2978000044822693},{"id":"https://openalex.org/C133338972","wikidata":"https://www.wikidata.org/wiki/Q2055750","display_name":"Compound Poisson process","level":4,"score":0.288100004196167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C197375991","wikidata":"https://www.wikidata.org/wiki/Q1464936","display_name":"Poisson manifold","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29782","pdf_url":"https://arxiv.org/pdf/2608.29782","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.2608.29782","doi":"https://doi.org/10.48550/arxiv.2608.29782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29782","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29782","pdf_url":"https://arxiv.org/pdf/2608.29782","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":[{"id":"https://openalex.org/G896127649","display_name":null,"funder_award_id":"12271265","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311213","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329998","display_name":"Nankai Zhide Foundation","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204886831.pdf","grobid_xml":"https://content.openalex.org/works/W7204886831.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7134060408","https://openalex.org/W4416260413","https://openalex.org/W4362561522","https://openalex.org/W2558726234","https://openalex.org/W4246528438","https://openalex.org/W4402011367","https://openalex.org/W2884911706","https://openalex.org/W2896932342","https://openalex.org/W4367297369","https://openalex.org/W4387604268"],"abstract_inverted_index":{"Poisson":[0,26,70,109,117],"algebras":[1,89,110],"are":[2,104],"the":[3,20,29,49,53,78],"quasiclassical":[4,30,102],"limits":[5,31,66,103,125],"of":[6,10,22,32,37,52,56,61,77,81,83,87,97,108,116],"associative":[7,12,88,98],"algebra":[8],"deformations":[9,36,82],"commutative":[11,38],"algebras.":[13,63],"This":[14],"paper":[15],"extends":[16],"this":[17],"process":[18,55,67],"to":[19],"level":[21],"bialgebras.":[23,43],"We":[24,120],"derive":[25],"bialgebras":[27,58],"as":[28,48,90,92],"antisymmetric":[33,41],"infinitesimal":[34,42],"bialgebra":[35,71],"and":[39,111],"cocommutative":[40],"It":[44],"might":[45],"be":[46],"regarded":[47],"``infinitesimal\"":[50],"version":[51],"quantization":[54],"Lie":[57],"in":[59,75],"terms":[60,76],"Hopf":[62],"Such":[64],"deformations-quasiclassical":[65,124],"for":[68],"a":[69,84,93,105,112],"is":[72],"equivalently":[73],"characterized":[74],"introduced":[79],"notions":[80],"matched":[85,106],"pair":[86,107],"well":[91],"standard":[94,113],"Manin":[95,114],"triple":[96,115],"algebras,":[99,118],"whose":[100],"corresponding":[101],"respectively.":[119],"illustrate":[121],"these":[122],"equivalent":[123],"processes":[126],"via":[127],"coherent":[128],"derivations.":[129]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-09-02T00:00:00"}