{"id":"https://openalex.org/W2096962143","doi":"https://doi.org/10.1112/s1461157014000102","title":"Gelfand\u2013Kirillov dimension of differential difference algebras","display_name":"Gelfand\u2013Kirillov dimension of differential difference algebras","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2096962143","doi":"https://doi.org/10.1112/s1461157014000102","mag":"2096962143"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157014000102","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000102","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/00C13F941033ACCC5A6DDDF1CE2A2EFB/S1461157014000102a.pdf/div-class-title-gelfand-kirillov-dimension-of-differential-difference-algebras-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/00C13F941033ACCC5A6DDDF1CE2A2EFB/S1461157014000102a.pdf/div-class-title-gelfand-kirillov-dimension-of-differential-difference-algebras-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101717393","display_name":"Yang Zhang","orcid":"https://orcid.org/0000-0001-8755-1806"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yang Zhang","raw_affiliation_strings":["Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email","University of MANITOBA (Canada)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email","institution_ids":["https://openalex.org/I46247651"]},{"raw_affiliation_string":"University of MANITOBA (Canada)","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065708851","display_name":"Xiangui Zhao","orcid":"https://orcid.org/0000-0001-7613-0539"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xiangui Zhao","raw_affiliation_strings":["Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email","University of MANITOBA (Canada)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 email","institution_ids":["https://openalex.org/I46247651"]},{"raw_affiliation_string":"University of MANITOBA (Canada)","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101717393"],"corresponding_institution_ids":["https://openalex.org/I46247651"],"apc_list":null,"apc_paid":null,"fwci":0.7361,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73971053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"1","first_page":"485","last_page":"495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9936000108718872,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9936000108718872,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9908999800682068,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9783999919891357,"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/mathematics","display_name":"Mathematics","score":0.9281952977180481},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7918062806129456},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6701239943504333},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6423835754394531},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5114278197288513},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.4165361225605011},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3734999895095825},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34144291281700134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2534208297729492},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.22769364714622498},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.07557904720306396}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9281952977180481},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7918062806129456},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6701239943504333},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6423835754394531},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5114278197288513},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.4165361225605011},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34144291281700134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2534208297729492},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.22769364714622498},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.07557904720306396},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/s1461157014000102","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000102","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/00C13F941033ACCC5A6DDDF1CE2A2EFB/S1461157014000102a.pdf/div-class-title-gelfand-kirillov-dimension-of-differential-difference-algebras-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1310.2583","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.2583","pdf_url":"https://arxiv.org/pdf/1310.2583","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1112/s1461157014000102","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000102","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/00C13F941033ACCC5A6DDDF1CE2A2EFB/S1461157014000102a.pdf/div-class-title-gelfand-kirillov-dimension-of-differential-difference-algebras-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2096962143.pdf","grobid_xml":"https://content.openalex.org/works/W2096962143.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1530431073","https://openalex.org/W1583871653","https://openalex.org/W1596655614","https://openalex.org/W1896783828","https://openalex.org/W1977049875","https://openalex.org/W1979306695","https://openalex.org/W1989543484","https://openalex.org/W1995253743","https://openalex.org/W2014595194","https://openalex.org/W2021406811","https://openalex.org/W2039225816","https://openalex.org/W2069738583","https://openalex.org/W2070295790","https://openalex.org/W2094156616","https://openalex.org/W2260131807","https://openalex.org/W2612451553","https://openalex.org/W4234736639"],"related_works":["https://openalex.org/W4303635220","https://openalex.org/W2066759926","https://openalex.org/W1652680335","https://openalex.org/W48612935","https://openalex.org/W4243865828","https://openalex.org/W173489679","https://openalex.org/W2021533431","https://openalex.org/W2074311814","https://openalex.org/W2963266233","https://openalex.org/W2071598674"],"abstract_inverted_index":{"Abstract":[0],"Differential":[1],"difference":[2,13,25,39],"algebras,":[3],"introduced":[4],"by":[5],"Mansfield":[6],"and":[7,41,66],"Szanto,":[8],"arose":[9],"naturally":[10],"from":[11],"differential":[12,24,38],"equations.":[14],"In":[15],"this":[16,59,73],"paper,":[17],"we":[18,52],"investigate":[19],"the":[20,33,47],"Gelfand\u2013Kirillov":[21,34,60],"dimension":[22,35,61],"of":[23,32,36,58],"algebras.":[26],"We":[27],"give":[28],"a":[29,37,42],"lower":[30,48],"bound":[31,49,57,75],"algebra":[40],"sufficient":[43],"condition":[44],"under":[45,62],"which":[46],"is":[50],"reached;":[51],"also":[53],"find":[54],"an":[55,68],"upper":[56,74],"some":[63],"specific":[64],"conditions":[65],"construct":[67],"example":[69],"to":[70],"show":[71],"that":[72],"cannot":[76],"be":[77],"sharpened":[78],"any":[79],"further.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
