{"id":"https://openalex.org/W7117581282","doi":"https://doi.org/10.48550/arxiv.2512.21971","title":"Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration","display_name":"Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration","publication_year":2025,"publication_date":"2025-12-26","ids":{"openalex":"https://openalex.org/W7117581282","doi":"https://doi.org/10.48550/arxiv.2512.21971"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.21971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21971","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.21971","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012346276","display_name":"Adrien Laurent","orcid":"https://orcid.org/0000-0002-4472-2908"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurent, Adrien Busnot","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121576860","display_name":"Yunnan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yunnan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5121530463","display_name":"Yunhe Sheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheng, Yunhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7300999760627747,"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":0.7300999760627747,"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":0.20170000195503235,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.01489999983459711,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/universal-enveloping-algebra","display_name":"Universal enveloping algebra","score":0.6780999898910522},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6570000052452087},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6133000254631042},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5791000127792358},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.574400007724762},{"id":"https://openalex.org/keywords/associative-algebra","display_name":"Associative algebra","score":0.5630000233650208},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5418000221252441},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5358999967575073},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.4359000027179718}],"concepts":[{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.6780999898910522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6654999852180481},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6570000052452087},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6133000254631042},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.574400007724762},{"id":"https://openalex.org/C51292594","wikidata":"https://www.wikidata.org/wiki/Q744960","display_name":"Associative algebra","level":5,"score":0.5630000233650208},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5418000221252441},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5358999967575073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5349000096321106},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.43560001254081726},{"id":"https://openalex.org/C176954179","wikidata":"https://www.wikidata.org/wiki/Q1052674","display_name":"Symmetric algebra","level":5,"score":0.39820000529289246},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.3765999972820282},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.36959999799728394},{"id":"https://openalex.org/C518143113","wikidata":"https://www.wikidata.org/wiki/Q4391941","display_name":"Non-associative algebra","level":4,"score":0.36550000309944153},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.33959999680519104},{"id":"https://openalex.org/C183222429","wikidata":"https://www.wikidata.org/wiki/Q42278","display_name":"Magma","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C115179944","wikidata":"https://www.wikidata.org/wiki/Q371133","display_name":"Incidence algebra","level":5,"score":0.32600000500679016},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.3255000114440918},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.31779998540878296},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C144091092","wikidata":"https://www.wikidata.org/wiki/Q3611543","display_name":"Graded Lie algebra","level":3,"score":0.26919999718666077},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.26739999651908875},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.2603999972343445},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.21971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21971","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.21971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21971","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,57],"introduce":[4],"the":[5,11,20,39,59,72],"notion":[6],"of":[7,22,33,43,76],"post-Hopf":[8,29,34,52],"algebroids,":[9],"generalizing":[10],"pre-Hopf":[12],"algebroids":[13,30],"introduced":[14],"in":[15,19,82],"[Bronasco,":[16],"Laurent,":[17],"2025]":[18],"study":[21],"exotic":[23],"aromatic":[24],"S-series.":[25],"We":[26,36],"construct":[27,58],"action":[28],"through":[31],"actions":[32],"algebras.":[35],"show":[37],"that":[38],"universal":[40],"enveloping":[41],"algebra":[42,46,62,66,75],"a":[44,51,55,64,68,77],"post-Lie-Rinehart":[45,61],"(post-Lie":[47],"algebroid)":[48],"is":[49],"naturally":[50],"algebroid.":[53],"As":[54],"byproduct,":[56],"free":[60],"using":[63],"magma":[65],"with":[67],"linear":[69],"map":[70],"to":[71],"derivation":[73],"Lie":[74],"commutative":[78],"associative":[79],"algebra.":[80],"Applications":[81],"geometric":[83],"numerical":[84],"integration":[85],"on":[86],"manifolds":[87],"are":[88],"given.":[89]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-30T00:00:00"}