{"id":"https://openalex.org/W1985501973","doi":"https://doi.org/10.1142/s0218196713400134","title":"ENVELOPING ALGEBRAS OF PRELIE ALGEBRAS, SOLOMON IDEMPOTENTS AND THE MAGNUS FORMULA","display_name":"ENVELOPING ALGEBRAS OF PRELIE ALGEBRAS, SOLOMON IDEMPOTENTS AND THE MAGNUS FORMULA","publication_year":2013,"publication_date":"2013-04-23","ids":{"openalex":"https://openalex.org/W1985501973","doi":"https://doi.org/10.1142/s0218196713400134","mag":"1985501973"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196713400134","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713400134","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1201.2159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014065986","display_name":"Fr\u00e9d\u00e9ric Chapoton","orcid":"https://orcid.org/0000-0001-8313-1644"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"FR\u00c9D\u00c9RIC CHAPOTON","raw_affiliation_strings":["Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Braconnier, 21 Avenue Claude Bernard, F-69622 Villeurbanne Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1, B\u00e2timent Braconnier, 21 Avenue Claude Bernard, F-69622 Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058944506","display_name":"Fr\u00e9d\u00e9ric Patras","orcid":"https://orcid.org/0000-0002-8098-8279"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"FR\u00c9D\u00c9RIC PATRAS","raw_affiliation_strings":["UMR 7351, CNRS, Universit\u00e9 de Nice, Parc Valrose, 06108 Nice Cedex 02, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UMR 7351, CNRS, Universit\u00e9 de Nice, Parc Valrose, 06108 Nice Cedex 02, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I201841394"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7332,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.92224991,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"04","first_page":"853","last_page":"861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9994999766349792,"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":0.9994999766349792,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.8784164190292358},{"id":"https://openalex.org/keywords/differential-algebra","display_name":"Differential algebra","score":0.6623698472976685},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.566541314125061},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49610885977745056},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48263320326805115},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47800412774086},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4229240119457245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06239813566207886}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8784164190292358},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.6623698472976685},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.566541314125061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49610885977745056},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48263320326805115},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47800412774086},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4229240119457245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06239813566207886},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196713400134","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713400134","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1201.2159","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.2159","pdf_url":"https://arxiv.org/pdf/1201.2159","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,"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":"pmh:oai:HAL:hal-00658228v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00658228","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Algebra and Computation, 2013, 23 (4), pp.853","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1201.2159","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1201.2159","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1201.2159","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.2159","pdf_url":"https://arxiv.org/pdf/1201.2159","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,"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W176448034","https://openalex.org/W1493137254","https://openalex.org/W1659648688","https://openalex.org/W1667848118","https://openalex.org/W1971509177","https://openalex.org/W1983373140","https://openalex.org/W1984396532","https://openalex.org/W1985467287","https://openalex.org/W2039763880","https://openalex.org/W2094709741","https://openalex.org/W2104410339","https://openalex.org/W2126692863","https://openalex.org/W2156466169","https://openalex.org/W2316225396","https://openalex.org/W2325419238","https://openalex.org/W2463297853","https://openalex.org/W2725469883","https://openalex.org/W2963373632","https://openalex.org/W3100690969","https://openalex.org/W3105839380","https://openalex.org/W4388320797"],"related_works":["https://openalex.org/W1484537289","https://openalex.org/W2912884769","https://openalex.org/W2071598674","https://openalex.org/W2951731112","https://openalex.org/W2148017112","https://openalex.org/W4392615856","https://openalex.org/W2963266233","https://openalex.org/W4301257383","https://openalex.org/W2352885086","https://openalex.org/W4312476787"],"abstract_inverted_index":{"We":[0,11],"study":[1],"the":[2,16,21,35,46,54,58,71],"internal":[3],"structure":[4],"of":[5,8,73],"enveloping":[6],"algebras":[7],"preLie":[9,59],"algebras.":[10],"show":[12,44],"in":[13,70,80],"particular":[14],"that":[15,45],"canonical":[17,55],"projections":[18],"arising":[19],"from":[20],"Poincar\u00e9\u2013Birkhoff\u2013Witt":[22],"theorem":[23],"can":[24],"be":[25,31],"computed":[26],"explicitly.":[27],"They":[28],"happen":[29],"to":[30,34,52],"closely":[32],"related":[33],"Magnus":[36,47],"formula":[37,48],"for":[38],"matrix":[39],"differential":[40,74],"equations.":[41],"Indeed,":[42],"we":[43],"provides":[49],"a":[50],"way":[51],"compute":[53],"projection":[56],"on":[57,67,77],"algebra.":[60],"Conversely,":[61],"our":[62],"results":[63],"provide":[64],"new":[65],"insights":[66],"classical":[68],"problems":[69],"theory":[72],"equations":[75],"and":[76],"recent":[78],"advances":[79],"their":[81],"combinatorial":[82],"understanding.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2022-09-26T00:00:00"}