{"id":"https://openalex.org/W2772012258","doi":"https://doi.org/10.48550/arxiv.1711.11234","title":"On Categories $\\mathcal{O}$ for Root-Reductive Lie Algebras","display_name":"On Categories $\\mathcal{O}$ for Root-Reductive Lie Algebras","publication_year":2017,"publication_date":"2017-11-30","ids":{"openalex":"https://openalex.org/W2772012258","doi":"https://doi.org/10.48550/arxiv.1711.11234","mag":"2772012258"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1711.11234","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.11234","pdf_url":"https://arxiv.org/pdf/1711.11234","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,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.11234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070973521","display_name":"Thanasin Nampaisarn","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nampaisarn, Thanasin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5070973521"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9750999808311462,"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":0.9750999808311462,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.013399999588727951,"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":0.008100000210106373,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/category-o","display_name":"category O","score":0.718999981880188},{"id":"https://openalex.org/keywords/finite-dimensional-weight-spaces","display_name":"finite-dimensional weight spaces","score":0.8069999814033508},{"id":"https://openalex.org/keywords/infinite-dimensional-lie-algebras","display_name":"infinite-dimensional Lie algebras","score":0.8920000195503235},{"id":"https://openalex.org/keywords/algebraically-closed-field-of-characteristic-zero","display_name":"algebraically closed field of characteristic zero","score":0.6819999814033508}],"concepts":[{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.801237940788269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7069901823997498},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.6911236643791199},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.67438143491745},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5462290048599243},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5380868911743164},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5240459442138672},{"id":"https://openalex.org/C13888372","wikidata":"https://www.wikidata.org/wiki/Q4944913","display_name":"Borel subgroup","level":3,"score":0.514426052570343},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.47240346670150757},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26944705843925476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20199856162071228},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.1573447287082672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.040572792291641235},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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":2,"locations":[{"id":"pmh:oai:arXiv.org:1711.11234","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.11234","pdf_url":"https://arxiv.org/pdf/1711.11234","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,"listed_in":[],"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":"doi:10.48550/arxiv.1711.11234","doi":"https://doi.org/10.48550/arxiv.1711.11234","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1711.11234","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,"listed_in":[],"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:1711.11234","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.11234","pdf_url":"https://arxiv.org/pdf/1711.11234","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,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W606654790","https://openalex.org/W1563456363","https://openalex.org/W1565930783","https://openalex.org/W1581189410","https://openalex.org/W1653987241","https://openalex.org/W1981527362","https://openalex.org/W1985215337","https://openalex.org/W1986825314","https://openalex.org/W2040838411","https://openalex.org/W2129442785"],"related_works":["https://openalex.org/W2120402312","https://openalex.org/W4301653177","https://openalex.org/W2962920011","https://openalex.org/W2535348549","https://openalex.org/W4297797709","https://openalex.org/W1983037845","https://openalex.org/W2951221230","https://openalex.org/W3174025154","https://openalex.org/W3101727915","https://openalex.org/W4390722472"],"abstract_inverted_index":{"Let":[0],"$\\mathfrak{g}$":[1],"be":[2],"a":[3,17,23],"root-reductive":[4,76],"Lie":[5,77],"algebra":[6],"over":[7],"an":[8,65],"algebraically":[9],"closed":[10],"field":[11],"$\\mathbb{K}$":[12],"of":[13,35,71],"characteristic":[14],"$0$":[15],"with":[16],"splitting":[18,24],"Borel":[19,54,59],"subalgebra":[20,27],"$\\mathfrak{b}$":[21],"containing":[22],"maximal":[25],"toral":[26],"$\\mathfrak{h}$.":[28],"We":[29],"study":[30],"the":[31,57,69],"category":[32],"$\\bar{\\mathcal{O}}$":[33],"consisting":[34],"all":[36],"$\\mathfrak{h}$-weight":[37,46],"$\\mathfrak{g}$-modules":[38],"which":[39],"are":[40],"locally":[41],"$\\mathfrak{b}$-finite":[42],"and":[43],"have":[44],"finite-dimensional":[45],"spaces.":[47],"The":[48],"focus":[49],"is":[50],"on":[51],"very":[52],"special":[53],"subalgebras":[55],"called":[56],"Dynkin":[58],"subalgebras.":[60],"This":[61],"paper":[62],"serves":[63],"as":[64],"initial":[66],"passage":[67],"to":[68],"understanding":[70],"categories":[72],"$\\mathcal{O}$":[73],"for":[74],"infinite-dimensional":[75],"algebras.":[78]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}