{"id":"https://openalex.org/W419688781","doi":"https://doi.org/10.1017/cbo9780511614910","title":"Lie Algebras of Finite and Affine Type","display_name":"Lie Algebras of Finite and Affine Type","publication_year":2005,"publication_date":"2005-10-27","ids":{"openalex":"https://openalex.org/W419688781","doi":"https://doi.org/10.1017/cbo9780511614910","mag":"419688781"},"language":"en","primary_location":{"id":"doi:10.1017/cbo9780511614910","doi":"https://doi.org/10.1017/cbo9780511614910","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511614910","pdf_url":null,"source":{"id":"https://openalex.org/S4306462995","display_name":"Cambridge University Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"monograph"},"volume":null,"type":"book","is_traditional":true,"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/A5075040292","display_name":"Roger Carter","orcid":"https://orcid.org/0000-0002-8513-0490","observed_orcids":["https://orcid.org/0000-0002-8513-0490"]},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Roger Carter","raw_affiliation_strings":["University of Warwick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075040292"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":2.3064,"has_fulltext":false,"cited_by_count":270,"citation_normalized_percentile":{"value":0.90776699,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"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":0.8877000212669373,"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":0.8877000212669373,"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":0.08389999717473984,"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":0.025200000032782555,"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/lie-algebras","display_name":"Lie algebras","score":0.9490000009536743},{"id":"https://openalex.org/keywords/finite-dimensional-simple-lie-algebras","display_name":"finite-dimensional simple Lie algebras","score":0.9020000100135803},{"id":"https://openalex.org/keywords/affine-lie-algebras","display_name":"affine Lie algebras","score":0.8429999947547913},{"id":"https://openalex.org/keywords/kac-moody-algebras","display_name":"Kac-Moody algebras","score":0.9919999837875366},{"id":"https://openalex.org/keywords/borcherds-algebras","display_name":"Borcherds algebras","score":0.9549999833106995},{"id":"https://openalex.org/keywords/classification-of-simple-lie-algebras","display_name":"classification of simple Lie algebras","score":0.8880000114440918},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.9509999752044678},{"id":"https://openalex.org/keywords/root-systems","display_name":"root systems","score":0.6209999918937683}],"concepts":[{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.7830454111099243},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6806788444519043},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6695519685745239},{"id":"https://openalex.org/C29945619","wikidata":"https://www.wikidata.org/wiki/Q856666","display_name":"Kac\u2013Moody algebra","level":5,"score":0.6021424531936646},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.5913623571395874},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5799329876899719},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5650840401649475},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5571907758712769},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5359886884689331},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5221338868141174},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.5071592330932617},{"id":"https://openalex.org/C66411559","wikidata":"https://www.wikidata.org/wiki/Q5532440","display_name":"Generalized Kac\u2013Moody algebra","level":5,"score":0.4248073995113373},{"id":"https://openalex.org/C145807718","wikidata":"https://www.wikidata.org/wiki/Q2004951","display_name":"Cartan matrix","level":5,"score":0.41222143173217773},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.25603824853897095},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/cbo9780511614910","doi":"https://doi.org/10.1017/cbo9780511614910","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511614910","pdf_url":null,"source":{"id":"https://openalex.org/S4306462995","display_name":"Cambridge University Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"monograph"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-013328139","doi":null,"is_oa":false,"landing_page_url":"http://bvbr.bib-bvb.de:8991/F?func=service&amp;doc_library=BVB01&amp;local_base=BVB01&amp;doc_number=013328139&amp;sequence=000001&amp;line_number=0001&amp;func_code=DB_RECORDS&amp;service_type=MEDIA","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:997380","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/997380","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W29642239","https://openalex.org/W782045910","https://openalex.org/W2129612323","https://openalex.org/W4213454814","https://openalex.org/W117451968","https://openalex.org/W2789709981","https://openalex.org/W198538526","https://openalex.org/W4243485707","https://openalex.org/W2163623225","https://openalex.org/W2406130871"],"abstract_inverted_index":{"Lie":[0,72,117],"algebras":[1,33,73,102],"have":[2],"many":[3],"varied":[4],"applications,":[5],"both":[6,25],"in":[7,45],"mathematics":[8],"and":[9,34,47,74,121],"mathematical":[10,19],"physics.":[11],"This":[12],"book":[13,63],"provides":[14],"a":[15,52,109],"thorough":[16],"but":[17],"relaxed":[18],"treatment":[20],"of":[21,29,39,55,61,67,75,87,94,100,111,115,119],"the":[22,26,35,48,62,68,85,112],"subject,":[23],"including":[24],"Cartan-Killing-Weyl":[27],"theory":[28,38,86],"finite":[30,69,77,120],"dimensional":[31,70,78],"simple":[32,71],"more":[36],"modern":[37],"Kac-Moody":[40,88],"algebras.":[41],"Proofs":[42],"are":[43],"given":[44],"detail":[46],"only":[49],"prerequisite":[50],"is":[51,103],"sound":[53],"knowledge":[54],"linear":[56],"algebra.":[57],"The":[58,81],"first":[59],"half":[60,83],"deals":[64],"with":[65],"classification":[66],"their":[76],"irreducible":[79],"representations.":[80],"second":[82],"introduces":[84],"algebras,":[89],"concentrating":[90],"particularly":[91],"on":[92],"those":[93],"affine":[95,122],"type.":[96,123],"A":[97],"brief":[98],"account":[99],"Borcherds":[101],"also":[104],"included.":[105],"An":[106],"Appendix":[107],"gives":[108],"summary":[110],"basic":[113],"properties":[114],"each":[116],"algebra":[118]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":15}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
