{"id":"https://openalex.org/W2056243371","doi":"https://doi.org/10.1145/1145768.1145778","title":"Implementation of Kumar's correspondence","display_name":"Implementation of Kumar's correspondence","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2056243371","doi":"https://doi.org/10.1145/1145768.1145778","mag":"2056243371"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145778","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/math/0601423v1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082066603","display_name":"Hirotachi Abo","orcid":"https://orcid.org/0000-0001-5630-1126"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I4210131357","https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hirotachi Abo","raw_affiliation_strings":["Colorado State University, Fort Collins, CO;"],"affiliations":[{"raw_affiliation_string":"Colorado State University, Fort Collins, CO;","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078621088","display_name":"Chris Peterson","orcid":"https://orcid.org/0000-0002-3982-6876"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I4210131357","https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chris Peterson","raw_affiliation_strings":["Colorado State University, Fort Collins, CO;"],"affiliations":[{"raw_affiliation_string":"Colorado State University, Fort Collins, CO;","institution_ids":["https://openalex.org/I92446798"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":61},"biblio":{"volume":null,"issue":null,"first_page":"9","last_page":"16"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Deformation Quantization of Poisson Manifolds","score":0.9995,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Deformation Quantization of Poisson Manifolds","score":0.9995,"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/T11680","display_name":"Proofs of Langlands Conjectures for GL(n)","score":0.9994,"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/T10061","display_name":"Algebraic Geometry and Moduli Theory","score":0.9987,"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/hyperplane","display_name":"Hyperplane","score":0.6939631},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.60263884},{"id":"https://openalex.org/keywords/moduli-theory","display_name":"Moduli Theory","score":0.454736},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4223534},{"id":"https://openalex.org/keywords/quaternionic-projective-space","display_name":"Quaternionic projective space","score":0.4154775}],"concepts":[{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.9272877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7543697},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6939631},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.6153021},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.60263884},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.5477809},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5175323},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.51058775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.49639946},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.47425973},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4319408},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4223534},{"id":"https://openalex.org/C84407019","wikidata":"https://www.wikidata.org/wiki/Q2724480","display_name":"Quaternionic projective space","level":5,"score":0.4154775},{"id":"https://openalex.org/C132702353","wikidata":"https://www.wikidata.org/wiki/Q2538404","display_name":"Complex projective space","level":4,"score":0.40198076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33487892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29497758},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1515482},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145778","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":null,"pdf_url":"http://arxiv.org/pdf/math/0601423v1.pdf","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"http://arxiv.org/abs/math/0601423","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":null,"pdf_url":"http://arxiv.org/pdf/math/0601423v1.pdf","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":13,"referenced_works":["https://openalex.org/W1589114936","https://openalex.org/W1685498048","https://openalex.org/W171488552","https://openalex.org/W1976129142","https://openalex.org/W1977055786","https://openalex.org/W1977361551","https://openalex.org/W1981482848","https://openalex.org/W1995209994","https://openalex.org/W1998033277","https://openalex.org/W2028590532","https://openalex.org/W2069699867","https://openalex.org/W2079285332","https://openalex.org/W2175098281"],"related_works":["https://openalex.org/W776110092","https://openalex.org/W764519735","https://openalex.org/W4233509437","https://openalex.org/W3104164025","https://openalex.org/W2964141497","https://openalex.org/W2725702466","https://openalex.org/W2294242384","https://openalex.org/W2079420241","https://openalex.org/W1994986044","https://openalex.org/W1977021162"],"abstract_inverted_index":{"In":[0],"1997,":[1],"N.M.":[2],"Kumar":[3,52],"published":[4],"a":[5,9,22,28,47,58,114,120],"paper":[6,102],"which":[7,39],"introduced":[8],"new":[10],"tool":[11],"of":[12,17,32,37,46,84,99,110],"use":[13],"in":[14,49,94,113,119],"the":[15,35,41,44,82,100],"construction":[16],"algebraic":[18],"vector":[19,23,61,67],"bundles.":[20],"Given":[21],"bundle":[24,42],"on":[25,43,63,69,91],"projective":[26,50,64,70,92],"n-space,":[27],"well":[29],"known":[30],"theorem":[31],"Quillen-Suslin":[33],"guarantees":[34],"existence":[36,83],"sections":[38],"generate":[40],"complement":[45],"hyperplane":[48],"n-space.":[51],"used":[53],"this":[54,78],"fact":[55],"to":[56,80,104],"give":[57,105],"correspondence":[59,79,112],"between":[60],"bundles":[62,68,90],"n-space":[65],"and":[66],"(n\u22121)-space":[71],"satisfying":[72],"certain":[73],"conditions.":[74],"He":[75],"then":[76],"applied":[77],"establish":[81],"many,":[85],"previously":[86],"unknown,":[87],"rank":[88],"two":[89],"fourspace":[93],"positive":[95],"characteristic.":[96],"The":[97],"goal":[98],"present":[101],"is":[103],"an":[106],"explicit":[107],"homological":[108],"description":[109],"Kumar's":[111],"setting":[115],"appropriate":[116],"for":[117],"implementation":[118],"computer":[121],"algebra":[122],"system.":[123]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2056243371","counts_by_year":[],"updated_date":"2024-11-30T18:50:25.978447","created_date":"2016-06-24"}