{"id":"https://openalex.org/W7147108144","doi":"https://doi.org/10.48550/arxiv.2603.28437","title":"The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods","display_name":"The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7147108144","doi":"https://doi.org/10.48550/arxiv.2603.28437"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.28437","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28437","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.2603.28437","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/A5044428884","display_name":"Hans Munthe-Kaas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Munthe-Kaas, Hans","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132588337","display_name":"Venkatesh G. S","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S, Venkatesh G.","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/T11416","display_name":"Numerical methods for differential equations","score":0.7817000150680542,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.7817000150680542,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.18310000002384186,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5437999963760376},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4514999985694885},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.450300008058548},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.426800012588501},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.41600000858306885},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4099000096321106},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4000000059604645},{"id":"https://openalex.org/keywords/geometric-series","display_name":"Geometric series","score":0.3815000057220459}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8356000185012817},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5437999963760376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46140000224113464},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.450300008058548},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.426800012588501},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C153363305","wikidata":"https://www.wikidata.org/wiki/Q1306887","display_name":"Geometric series","level":3,"score":0.3815000057220459},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3587000072002411},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32420000433921814},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.28437","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28437","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.2603.28437","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28437","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":{"Aromatic":[0],"Butcher":[1],"series":[2],"were":[3,38],"successfully":[4],"introduced":[5],"for":[6,57,82],"the":[7,42,52,58,74],"study":[8,59],"and":[9,31,35,79],"design":[10],"of":[11,54,60,97],"numerical":[12],"integrators":[13,62],"that":[14,71,87],"preserve":[15,88],"volume":[16],"while":[17],"solving":[18],"differential":[19],"equations":[20],"in":[21],"Euclidean":[22],"spaces.":[23],"They":[24],"are":[25],"naturally":[26],"associated":[27],"to":[28,40,93],"pre-Lie-Rinehart":[29,45],"algebras":[30],"pre-Hopf":[32],"algebroids":[33],"structures,":[34],"aromatic":[36,55,68],"trees":[37,56],"shown":[39],"form":[41],"free":[43,75],"tracial":[44,76],"algebra.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50],"present":[51],"generalisation":[53],"divergence-free":[61,90],"on":[63],"manifolds.":[64],"We":[65],"introduce":[66],"planar":[67],"trees,":[69],"prove":[70],"they":[72],"span":[73],"post-Lie-Rinehart":[77],"algebra,":[78],"apply":[80],"them":[81],"deriving":[83],"new":[84],"Lie-group":[85],"methods":[86],"geometric":[89],"features":[91],"up":[92],"a":[94],"high":[95],"order":[96],"accuracy.":[98]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-02T00:00:00"}
