{"id":"https://openalex.org/W2071038091","doi":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","title":"Spectral Symmetry of the Dirac Operator in the Presence of a Group Action","display_name":"Spectral Symmetry of the Dirac Operator in the Presence of a Group Action","publication_year":1993,"publication_date":"1993-02-01","ids":{"openalex":"https://openalex.org/W2071038091","doi":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","mag":"2071038091"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1993-1075381-x","doi":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","pdf_url":"https://www.ams.org/tran/1993-335-02/S0002-9947-1993-1075381-X/S0002-9947-1993-1075381-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1993-335-02/S0002-9947-1993-1075381-X/S0002-9947-1993-1075381-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076609030","display_name":"Howard D. Fegan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. D. Fegan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113060212","display_name":"B. Steer","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Steer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.24979855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"335","issue":"2","first_page":"631","last_page":"631"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.4406999945640564,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.4406999945640564,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.21799999475479126,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.08179999887943268,"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/dirac-operator","display_name":"Dirac operator","score":0.9869999885559082},{"id":"https://openalex.org/keywords/spectral-symmetry","display_name":"spectral symmetry","score":0.9010000228881836},{"id":"https://openalex.org/keywords/compact-lie-group-actions","display_name":"compact Lie group actions","score":0.7429999709129333},{"id":"https://openalex.org/keywords/spin-manifolds","display_name":"spin manifolds","score":0.8650000095367432},{"id":"https://openalex.org/keywords/isometric-group-actions","display_name":"isometric group actions","score":0.7699999809265137},{"id":"https://openalex.org/keywords/levi-civita-connection","display_name":"Levi-Civita connection","score":0.9200000166893005},{"id":"https://openalex.org/keywords/eta-invariant","display_name":"eta invariant","score":0.3019999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.883622407913208},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.7488408088684082},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.7416390776634216},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.631756067276001},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6106065511703491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5696592926979065},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5451263189315796},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5388201475143433},{"id":"https://openalex.org/C49976459","wikidata":"https://www.wikidata.org/wiki/Q17103517","display_name":"Spectral triple","level":4,"score":0.5299333930015564},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.528947114944458},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5165632963180542},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5026988983154297},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.49213212728500366},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4768058955669403},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4750654399394989},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4622265100479126},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.4516167640686035},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4415208697319031},{"id":"https://openalex.org/C2779728059","wikidata":"https://www.wikidata.org/wiki/Q3687052","display_name":"Spin connection","level":3,"score":0.4296034574508667},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.4290008842945099},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26406821608543396},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20909282565116882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15947139263153076},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13227835297584534},{"id":"https://openalex.org/C29384965","wikidata":"https://www.wikidata.org/wiki/Q7049223","display_name":"Noncommutative quantum field theory","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9947-1993-1075381-x","doi":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","pdf_url":"https://www.ams.org/tran/1993-335-02/S0002-9947-1993-1075381-X/S0002-9947-1993-1075381-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2154397","doi":"https://doi.org/10.2307/2154397","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2154397","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-1993-1075381-x","doi":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1993-1075381-x","pdf_url":"https://www.ams.org/tran/1993-335-02/S0002-9947-1993-1075381-X/S0002-9947-1993-1075381-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071038091.pdf","grobid_xml":"https://content.openalex.org/works/W2071038091.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W49952276","https://openalex.org/W1535294931","https://openalex.org/W1914665694","https://openalex.org/W2022036502","https://openalex.org/W2030673730","https://openalex.org/W2040542969","https://openalex.org/W2049274587","https://openalex.org/W2073112363","https://openalex.org/W2127494126","https://openalex.org/W2146205407","https://openalex.org/W2168713092","https://openalex.org/W6634539492"],"related_works":["https://openalex.org/W2320003244","https://openalex.org/W2032317421","https://openalex.org/W7095291266","https://openalex.org/W2057184979","https://openalex.org/W1969400868","https://openalex.org/W2079016147","https://openalex.org/W2884654405","https://openalex.org/W2166370489","https://openalex.org/W3127227959","https://openalex.org/W4392427681"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2],"a":[3,15,58],"compact":[4],"Lie":[5],"group":[6],"of":[7,19,60,66],"rank":[8],"two":[9],"or":[10],"greater":[11],"which":[12,63],"acts":[13],"on":[14,38,102],"spin":[16],"manifold":[17],"$M$":[18,39],"dimension":[20],"$4k":[21],"+":[22],"3$":[23],"through":[24],"isometries":[25],"with":[26],"finite":[27],"isotropy":[28],"subgroups":[29],"at":[30,98],"each":[31],"point.":[32],"Define":[33],"the":[34,42,76,84,90,93],"Dirac":[35],"operator,":[36],"$P$,":[37],"relative":[40],"to":[41,74],"split":[43],"connection.":[44],"Then":[45],"we":[46,81],"show":[47,87],"that":[48,88],"$P$":[49],"has":[50],"spectral":[51],"$G$-symmetry.":[52],"This":[53],"is":[54,100],"first":[55],"established":[56],"in":[57,68],"number":[59],"special":[61],"cases":[62],"are":[64],"both":[65],"interest":[67],"their":[69],"own":[70],"right":[71],"and":[72,86],"necessary":[73],"establish":[75],"more":[77],"general":[78],"case.":[79],"Finally":[80],"consider":[82],"changing":[83],"connection":[85,92],"for":[89],"Levi-Civita":[91],"equivariant":[94],"eta":[95],"function":[96],"evaluated":[97],"zero":[99],"constant":[101],"$G$.":[103]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}