{"id":"https://openalex.org/W2045853812","doi":"https://doi.org/10.1142/s0218196713500069","title":"ON THE DIMENSION OF PRODUCTS OF HOMOGENEOUS SUBSPACES IN FREE LIE ALGEBRAS","display_name":"ON THE DIMENSION OF PRODUCTS OF HOMOGENEOUS SUBSPACES IN FREE LIE ALGEBRAS","publication_year":2012,"publication_date":"2012-12-26","ids":{"openalex":"https://openalex.org/W2045853812","doi":"https://doi.org/10.1142/s0218196713500069","mag":"2045853812"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196713500069","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713500069","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083126516","display_name":"Nil Mansuro\u011flu","orcid":"https://orcid.org/0000-0002-6400-2115"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"NIL MANSURO\u01e6LU","raw_affiliation_strings":["School of Mathematics University of Manchester, Alan Turing Building, Manchester, M13 9PL, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics University of Manchester, Alan Turing Building, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049710697","display_name":"Ralph St\u00f6hr","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"RALPH ST\u00d6HR","raw_affiliation_strings":["School of Mathematics University of Manchester, Alan Turing Building, Manchester, M13 9PL, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics University of Manchester, Alan Turing Building, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083126516"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":0.573,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61852093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"01","first_page":"205","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9995999932289124,"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":0.9995999932289124,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9987000226974487,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9976000189781189,"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/mathematics","display_name":"Mathematics","score":0.8955323696136475},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8629641532897949},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.804840087890625},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.634716272354126},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6204776763916016},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5752072930335999},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5556985139846802},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.5438443422317505},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.532502293586731},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4998898506164551},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3994046151638031},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07334849238395691},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06192612648010254}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8955323696136475},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8629641532897949},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.804840087890625},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.634716272354126},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6204776763916016},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5752072930335999},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5556985139846802},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.5438443422317505},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.532502293586731},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4998898506164551},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3994046151638031},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07334849238395691},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06192612648010254},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196713500069","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713500069","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:eprints.maths.manchester.ac.uk.MIMS.EPrints:1955","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/27d734d1-0528-4ed8-81c7-9109566df9ad","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/27d734d1-0528-4ed8-81c7-9109566df9ad","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mansuroglu, N, Mansurolu, N & St\u00f6hr, R 2013, 'On the dimension of products of homogeneous subspaces in free lie algebras', International Journal of Algebra and Computation, vol. 23, no. 1, pp. 205-213. https://doi.org/10.1142/S0218196713500069","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.atira.dk:publications/27d734d1-0528-4ed8-81c7-9109566df9ad","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/on-the-dimension-of-products-of-homogeneous-subspaces-in-free-lie-algebras(27d734d1-0528-4ed8-81c7-9109566df9ad).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mansuroglu, N, Mansurolu, N & St\u00f6hr, R 2013, 'On the dimension of products of homogeneous subspaces in free lie algebras', International Journal of Algebra and Computation, vol. 23, no. 1, pp. 205-213. https://doi.org/10.1142/S0218196713500069","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W157718562","https://openalex.org/W195873805","https://openalex.org/W1510024482","https://openalex.org/W1516116134","https://openalex.org/W1970098594","https://openalex.org/W1975714928","https://openalex.org/W1986464780","https://openalex.org/W2001713351"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2896134808","https://openalex.org/W4211228991","https://openalex.org/W2949110394","https://openalex.org/W2353790329","https://openalex.org/W2279743781","https://openalex.org/W140666874","https://openalex.org/W1978233018","https://openalex.org/W4289378085","https://openalex.org/W2372627074"],"abstract_inverted_index":{"Let":[0],"L":[1,16,36,65,68,75,78,116,119,151,154,187,190],"be":[2],"a":[3,11,88],"free":[4],"Lie":[5],"algebra":[6],"of":[7,24,30,59,87,90,96,104,112,124,134,147,177,183,195],"finite":[8],"rank":[9],"over":[10,122,132],"field":[12,106],"K":[13],"and":[14,42,50,163,179],"let":[15],"n":[17,21,37,43,66,76,152,162,188],"denote":[18],"the":[19,28,31,47,60,85,94,102,105,110,130,145,175,181],"degree":[20],"homogeneous":[22,92],"component":[23],"L.":[25],"Formulae":[26],"for":[27,39,144],"dimension":[29,95,111,131,146,182,197],"subspaces":[32,58],"[L":[33,62,113,148,184],"m":[34,41,63,73,149,185],",":[35,64,67,74,115,118,150,153,186,189],"]":[38,70,121,192],"all":[40],"were":[44],"obtained":[45],"by":[46],"second":[48],"author":[49],"Michael":[51],"Vaughan-Lee.":[52],"In":[53],"this":[54],"note":[55],"we":[56],"consider":[57],"form":[61],"k":[69,79,155,164,191],"=":[71],"[[L":[72],"],":[77],"].":[80,156],"Surprisingly,":[81],"in":[82,193],"contrast":[83],"to":[84,167],"case":[86],"product":[89],"two":[91],"components,":[93],"such":[97],"products":[98],"may":[99],"depend":[100,173],"on":[101,160,174],"characteristic":[103,125,135,176],"K.":[107],"For":[108],"example,":[109],"2":[114,117,126],"1":[120],"fields":[123,133],"is":[127],"different":[128],"from":[129],"other":[136],"than":[137],"2.":[138],"Our":[139],"main":[140],"results":[141],"are":[142],"formulae":[143,169],"Under":[157],"certain":[158],"conditions":[159],"m,":[161],"they":[165],"lead":[166],"explicit":[168],"that":[170],"do":[171],"not":[172],"K,":[178],"express":[180],"terms":[194],"Witt's":[196],"function.":[198]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}