{"id":"https://openalex.org/W1925644118","doi":"https://doi.org/10.48550/arxiv.0902.0431","title":"Exceptional Lie groups","display_name":"Exceptional Lie groups","publication_year":2009,"publication_date":"2009-02-03","ids":{"openalex":"https://openalex.org/W1925644118","doi":"https://doi.org/10.48550/arxiv.0902.0431","mag":"1925644118"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0902.0431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0902.0431","pdf_url":"https://arxiv.org/pdf/0902.0431","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/0902.0431","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017476313","display_name":"Ichiro Yokota","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yokota, Ichiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017476313"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":70,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9945999979972839,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9945999979972839,"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":0.0017999999690800905,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.00139999995008111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exceptional-lie-groups","display_name":"exceptional Lie groups","score":0.9789999723434448},{"id":"https://openalex.org/keywords/compact-simple-lie-groups","display_name":"compact simple Lie groups","score":0.7549999952316284},{"id":"https://openalex.org/keywords/involutive-automorphisms","display_name":"involutive automorphisms","score":0.8840000033378601},{"id":"https://openalex.org/keywords/fixed-point-subgroups","display_name":"fixed point subgroup","score":0.8920000195503235},{"id":"https://openalex.org/keywords/compact-symmetric-spaces","display_name":"compact symmetric spaces","score":0.968999981880188},{"id":"https://openalex.org/keywords/classification-of-lie-groups","display_name":"classification of Lie groups","score":0.6589999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7827122807502747},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.7544571161270142},{"id":"https://openalex.org/C22365015","wikidata":"https://www.wikidata.org/wiki/Q1003162","display_name":"Simple Lie group","level":3,"score":0.6717555522918701},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6138393878936768},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6085822582244873},{"id":"https://openalex.org/C197893656","wikidata":"https://www.wikidata.org/wiki/Q1000120","display_name":"Maximal torus","level":5,"score":0.5514222979545593},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5392097234725952},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.4968147575855255},{"id":"https://openalex.org/C143135876","wikidata":"https://www.wikidata.org/wiki/Q357300","display_name":"Lie theory","level":5,"score":0.4592997133731842},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.43455737829208374},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.4249623417854309},{"id":"https://openalex.org/C139941754","wikidata":"https://www.wikidata.org/wiki/Q3058244","display_name":"Symmetric space","level":2,"score":0.41670089960098267},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4118073880672455},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3519766330718994},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34962600469589233},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.3176242709159851},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.2575804591178894},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13567590713500977},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.12966102361679077},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.09444168210029602},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.044288843870162964},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:0902.0431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0902.0431","pdf_url":"https://arxiv.org/pdf/0902.0431","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.0902.0431","doi":"https://doi.org/10.48550/arxiv.0902.0431","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0902.0431","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:0902.0431","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0902.0431","pdf_url":"https://arxiv.org/pdf/0902.0431","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":8,"referenced_works":["https://openalex.org/W118430899","https://openalex.org/W1565930783","https://openalex.org/W1969545359","https://openalex.org/W1983311571","https://openalex.org/W2020495917","https://openalex.org/W2064410071","https://openalex.org/W2076620126","https://openalex.org/W2330591831"],"related_works":["https://openalex.org/W2018327016","https://openalex.org/W85062688","https://openalex.org/W2024602374","https://openalex.org/W1569946559","https://openalex.org/W3141422206","https://openalex.org/W2766897805","https://openalex.org/W2030543496","https://openalex.org/W2094790813","https://openalex.org/W4213347370","https://openalex.org/W2085933554"],"abstract_inverted_index":{"We":[0,13],"describe":[1],"simply":[2,17],"connected":[3,18],"compact":[4,19,51],"exceptional":[5,20,55],"simple":[6],"Lie":[7,21,68],"groups":[8,22],"in":[9,94],"very":[10],"elementary":[11],"way.":[12],"first":[14],"construct":[15],"all":[16,28,49,65],"G":[23],"concretely.":[24],"Next,":[25],"we":[26,71,86],"find":[27],"involutive":[29],"automorphisms":[30],"of":[31,38,48,54,64,76,80],"G,":[32],"and":[33,57,96],"determine":[34],"the":[35,39,46,73,77],"group":[36,74],"structures":[37,75],"fixed":[40],"points":[41],"subgroup.":[42],"They":[43],"correspond":[44,61],"to":[45,62,91],"classification":[47,63],"irreducible":[50],"symmetric":[52],"spaces":[53],"type,":[56],"that":[58],"they":[59],"also":[60],"non-compact":[66],"exceptionalsimple":[67],"groups.":[69],"Finally,":[70],"determined":[72],"maximal":[78,81],"subgroups":[79],"rank.":[82],"At":[83],"any":[84],"rate,":[85],"would":[87],"like":[88],"this":[89],"book":[90],"be":[92],"used":[93],"mathematics":[95],"physics.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":8}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
