{"id":"https://openalex.org/W99237326","doi":null,"title":"Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists","display_name":"Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists","publication_year":1997,"publication_date":"1997-07-24","ids":{"openalex":"https://openalex.org/W99237326","mag":"99237326"},"language":"en","primary_location":{"id":"pmh:oai:cds.cern.ch:332105","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/332105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400735","display_name":"International Linear Collider","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5010774456","display_name":"J\u00fcrgen Fuchs","orcid":"https://orcid.org/0000-0003-4081-6234","observed_orcids":["https://orcid.org/0000-0003-4081-6234"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Fuchs","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4081-6234","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076428287","display_name":"Christoph Schweigert B","orcid":"https://orcid.org/0000-0003-1342-6230","observed_orcids":["https://orcid.org/0000-0003-1342-6230"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Schweigert","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1342-6230","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6601,"has_fulltext":false,"cited_by_count":168,"citation_normalized_percentile":{"value":0.92064005,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"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":0.6782000064849854,"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":0.6782000064849854,"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":0.22349999845027924,"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":0.08860000222921371,"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":1.0},{"id":"https://openalex.org/keywords/representation-theory-of-lie-groups","display_name":"representation theory of Lie groups","score":0.8220000267028809},{"id":"https://openalex.org/keywords/simple-lie-algebras","display_name":"simple Lie algebras","score":0.9649999737739563},{"id":"https://openalex.org/keywords/affine-lie-algebras","display_name":"affine Lie algebras","score":0.9990000128746033},{"id":"https://openalex.org/keywords/real-forms","display_name":"real forms","score":0.7860000133514404},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.9909999966621399},{"id":"https://openalex.org/keywords/loop-algebras","display_name":"loop algebras","score":0.8980000019073486},{"id":"https://openalex.org/keywords/highest-weight-representations","display_name":"highest weight representations","score":0.9990000128746033},{"id":"https://openalex.org/keywords/verma-modules","display_name":"Verma modules","score":0.9990000128746033},{"id":"https://openalex.org/keywords/casimir-operators","display_name":"Casimir operators","score":0.8830000162124634},{"id":"https://openalex.org/keywords/clebsch-gordan-coefficients","display_name":"Clebsch-Gordan coefficients","score":0.9309999942779541},{"id":"https://openalex.org/keywords/invariant-tensors","display_name":"invariant tensors","score":0.7749999761581421},{"id":"https://openalex.org/keywords/branching-rules","display_name":"branching rules","score":0.8759999871253967},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.9990000128746033},{"id":"https://openalex.org/keywords/spinors","display_name":"spinors","score":0.996999979019165},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.9990000128746033},{"id":"https://openalex.org/keywords/supersymmetry","display_name":"supersymmetry","score":1.0},{"id":"https://openalex.org/keywords/hopf-algebras","display_name":"Hopf algebras","score":0.9990000128746033},{"id":"https://openalex.org/keywords/representation-ring","display_name":"representation ring","score":0.9570000171661377}],"concepts":[{"id":"https://openalex.org/C186489112","wikidata":"https://www.wikidata.org/wiki/Q763735","display_name":"Representation of a Lie group","level":3,"score":0.5985156893730164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5653177499771118},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.5626954436302185},{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.527809739112854},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.5205477476119995},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5182949900627136},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.49593386054039},{"id":"https://openalex.org/C66411559","wikidata":"https://www.wikidata.org/wiki/Q5532440","display_name":"Generalized Kac\u2013Moody algebra","level":5,"score":0.4722423255443573},{"id":"https://openalex.org/C518143113","wikidata":"https://www.wikidata.org/wiki/Q4391941","display_name":"Non-associative algebra","level":4,"score":0.4650982618331909},{"id":"https://openalex.org/C99634282","wikidata":"https://www.wikidata.org/wiki/Q634557","display_name":"Killing form","level":5,"score":0.4642871618270874},{"id":"https://openalex.org/C29945619","wikidata":"https://www.wikidata.org/wiki/Q856666","display_name":"Kac\u2013Moody algebra","level":5,"score":0.45784538984298706},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.45766618847846985},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44602739810943604},{"id":"https://openalex.org/C189612460","wikidata":"https://www.wikidata.org/wiki/Q7921510","display_name":"Verma module","level":3,"score":0.4355725646018982},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.4258015751838684},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.4058239758014679},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09618273377418518},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.08461853861808777},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.07466703653335571}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:cds.cern.ch:332105","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/332105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400735","display_name":"International Linear Collider","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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},{"id":"mag:99237326","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/ncid/BA32253746","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W615459935","https://openalex.org/W7029968652","https://openalex.org/W1493272590","https://openalex.org/W1549429185","https://openalex.org/W4234366929","https://openalex.org/W4233500748","https://openalex.org/W2538950179","https://openalex.org/W2766994147","https://openalex.org/W4402590320","https://openalex.org/W7096546809"],"abstract_inverted_index":{"This":[0],"is":[1,119,141],"an":[2],"introduction":[3,43],"to":[4,38,44,76,147],"Lie":[5,18,45,57,62,133],"algebras":[6,19,46,69,102,111,134],"and":[7,27,47,55,61,70,89,95,103,109,112,121,124],"their":[8,33,48],"applications":[9],"in":[10,135],"physics.":[11],"The":[12,139],"first":[13],"three":[14],"chapters":[15],"show":[16],"how":[17],"arise":[20],"naturally":[21],"from":[22],"symmetries":[23],"of":[24,32,132],"physical":[25,137],"systems":[26],"illustrate":[28,129],"through":[29],"examples":[30,125],"much":[31],"general":[34],"structure.":[35],"Chapters":[36,74],"4":[37],"13":[39],"give":[40],"a":[41,144,154],"detailed":[42,116],"representations,":[49],"covering":[50],"the":[51,64,127,130],"Cartan-Weyl":[52],"basis,":[53],"simple":[54],"affine":[56],"algebras,":[58],"real":[59,136],"forms":[60],"groups,":[63],"Weyl":[65],"group,":[66],"automorphisms,":[67],"loop":[68],"highest":[71],"weight":[72],"representations.":[73],"14":[75],"22":[77],"cover":[78],"specific":[79],"further":[80],"topics,":[81],"such":[82],"as":[83],"Verma":[84],"modules,":[85],"Casimirs,":[86],"tensor":[87],"products":[88],"Clebsch-Gordan":[90],"coefficients,":[91],"invariant":[92],"tensors,":[93],"subalgebras":[94],"branching":[96],"rules,":[97],"Young":[98],"tableaux,":[99],"spinors,":[100],"Clifford":[101],"supersymmetry,":[104],"representations":[105],"on":[106],"function":[107],"spaces,":[108],"Hopf":[110],"representation":[113],"rings.":[114],"A":[115],"reference":[117,156],"list":[118],"provided,":[120],"many":[122],"exercises":[123],"throughout":[126],"book":[128],"use":[131],"problems.":[138],"text":[140],"written":[142],"at":[143],"level":[145],"accessible":[146],"graduate":[148],"students,":[149],"but":[150],"will":[151],"also":[152],"provide":[153],"comprehensive":[155],"for":[157],"researchers.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":5}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}