{"id":"https://openalex.org/W2090651691","doi":"https://doi.org/10.1142/s0218196799000291","title":"ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS","display_name":"ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W2090651691","doi":"https://doi.org/10.1142/s0218196799000291","mag":"2090651691"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196799000291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196799000291","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/A5068025443","display_name":"Antonio Giambruno","orcid":"https://orcid.org/0000-0002-3422-2539"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"A. GIAMBRUNO","raw_affiliation_strings":["Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Palermo, 90123 Palermo, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Applicazioni, Universit\u00e0 di Palermo, 90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058483288","display_name":"\u0421. \u041f. \u041c\u0438\u0449\u0435\u043d\u043a\u043e","orcid":"https://orcid.org/0000-0002-8635-4234"},"institutions":[{"id":"https://openalex.org/I194437852","display_name":"Ulyanovsk State University","ror":"https://ror.org/02vn11j58","country_code":"RU","type":"education","lineage":["https://openalex.org/I194437852"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"S. MISHCHENKO","raw_affiliation_strings":["Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk\u00a0432100, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk\u00a0432100, Russia","institution_ids":["https://openalex.org/I194437852"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068063278","display_name":"Mikhail Zaicev","orcid":"https://orcid.org/0000-0002-5862-0101"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"M. ZAICEV","raw_affiliation_strings":["Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University,  Moscow, 119899, Russia","Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University,  Moscow, 119899, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068025443"],"corresponding_institution_ids":["https://openalex.org/I900890020"],"apc_list":null,"apc_paid":null,"fwci":2.18,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.87142187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"09","issue":"05","first_page":"483","last_page":"491"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9997000098228455,"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":0.9997000098228455,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9962000250816345,"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/T10849","display_name":"Finite Group Theory Research","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8797515630722046},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.8114075064659119},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6240852475166321},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5335918664932251},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5166752338409424},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.48931214213371277},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.47462737560272217},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.4518886208534241},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4344383478164673},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3320387899875641},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06577137112617493}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8797515630722046},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.8114075064659119},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6240852475166321},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5335918664932251},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5166752338409424},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.48931214213371277},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.47462737560272217},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4518886208534241},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4344383478164673},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3320387899875641},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06577137112617493},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196799000291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196799000291","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1968195486","https://openalex.org/W1983484943","https://openalex.org/W2028404788","https://openalex.org/W2068024066","https://openalex.org/W2117933272","https://openalex.org/W2125838758","https://openalex.org/W2134984950"],"related_works":["https://openalex.org/W4230581126","https://openalex.org/W4378765297","https://openalex.org/W2761548024","https://openalex.org/W2016521071","https://openalex.org/W2001367988","https://openalex.org/W2069384021","https://openalex.org/W1990308498","https://openalex.org/W1986629578","https://openalex.org/W2149075715","https://openalex.org/W2352206503"],"abstract_inverted_index":{"We":[0,20],"study":[1],"the":[2,9,25,29,60,66],"variety":[3],"of":[4,17,34,62,69],"Lie":[5],"algebras":[6],"defined":[7],"by":[8],"identity":[10],"[Formula:":[11,79],"see":[12,80],"text]":[13],"over":[14],"a":[15],"field":[16],"characteristic":[18],"zero.":[19],"prove":[21],"that,":[22],"as":[23],"in":[24,28,72],"associative":[26],"case,":[27],"nth":[30],"cocharacter":[31],"\u03c7":[32,73],"n":[33,40,50,74],"this":[35,63],"variety,":[36,64],"every":[37],"irreducible":[38],"S":[39],"-character":[41],"appears":[42],"with":[43],"polynomially":[44],"bounded":[45],"multiplicity":[46],"(not":[47],"greater":[48],"than":[49],"2":[51],").":[52],"Anyway,":[53],"surprisingly":[54],"enough,":[55],"we":[56],"also":[57],"show":[58],"that":[59],"colength":[61],"i.e.":[65],"total":[67],"number":[68],"irreducibles":[70],"appearing":[71],"is":[75],"asymptotically":[76],"equal":[77],"to":[78],"text].":[81]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
