{"id":"https://openalex.org/W3025200532","doi":"https://doi.org/10.3390/sym12050817","title":"SU(2) \u00d7 SU(2) Algebras and the Lorentz Group O(3,3)","display_name":"SU(2) \u00d7 SU(2) Algebras and the Lorentz Group O(3,3)","publication_year":2020,"publication_date":"2020-05-15","ids":{"openalex":"https://openalex.org/W3025200532","doi":"https://doi.org/10.3390/sym12050817","mag":"3025200532"},"language":"en","primary_location":{"id":"doi:10.3390/sym12050817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050817","pdf_url":"https://www.mdpi.com/2073-8994/12/5/817/pdf?version=1589536200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/5/817/pdf?version=1589536200","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081653507","display_name":"Martin Walker","orcid":"https://orcid.org/0000-0002-6793-3775"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Walker","raw_affiliation_strings":["Independent Researcher, 3958 Grandis Place, Victoria, BC V8N 4H6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, 3958 Grandis Place, Victoria, BC V8N 4H6, Canada","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5081653507"],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04556899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"5","first_page":"817","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9674000144004822,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11414","display_name":"Quantum optics and atomic interactions","score":0.9674000144004822,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12748","display_name":"Molecular spectroscopy and chirality","score":0.96670001745224,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9587000012397766,"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/lorentz-transformation","display_name":"Lorentz transformation","score":0.6691532731056213},{"id":"https://openalex.org/keywords/special-unitary-group","display_name":"Special unitary group","score":0.6239140629768372},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6099553108215332},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5786730051040649},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5535505414009094},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5199731588363647},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.5039762854576111},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.48802414536476135},{"id":"https://openalex.org/keywords/rotation-group-so","display_name":"Rotation group SO","score":0.43523919582366943},{"id":"https://openalex.org/keywords/structure-constants","display_name":"Structure constants","score":0.43417099118232727},{"id":"https://openalex.org/keywords/lorentz-group","display_name":"Lorentz group","score":0.42674171924591064},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4090847969055176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38839036226272583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3645336329936981},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2126012146472931},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08378589153289795}],"concepts":[{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.6691532731056213},{"id":"https://openalex.org/C32955637","wikidata":"https://www.wikidata.org/wiki/Q684363","display_name":"Special unitary group","level":2,"score":0.6239140629768372},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6099553108215332},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5786730051040649},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5535505414009094},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5199731588363647},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.5039762854576111},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.48802414536476135},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.43523919582366943},{"id":"https://openalex.org/C2777394768","wikidata":"https://www.wikidata.org/wiki/Q7625098","display_name":"Structure constants","level":2,"score":0.43417099118232727},{"id":"https://openalex.org/C150523333","wikidata":"https://www.wikidata.org/wiki/Q1334417","display_name":"Lorentz group","level":3,"score":0.42674171924591064},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4090847969055176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38839036226272583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3645336329936981},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2126012146472931},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08378589153289795}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym12050817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050817","pdf_url":"https://www.mdpi.com/2073-8994/12/5/817/pdf?version=1589536200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c85c7530c2be401790af0c23eec2f45f","is_oa":true,"landing_page_url":"https://doaj.org/article/c85c7530c2be401790af0c23eec2f45f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 5, p 817 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym12050817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12050817","pdf_url":"https://www.mdpi.com/2073-8994/12/5/817/pdf?version=1589536200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3025200532.pdf","grobid_xml":"https://content.openalex.org/works/W3025200532.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1479818201","https://openalex.org/W1974167433","https://openalex.org/W2029921350","https://openalex.org/W2963556828","https://openalex.org/W4235337103","https://openalex.org/W4237598729","https://openalex.org/W4243055393"],"related_works":["https://openalex.org/W2004494759","https://openalex.org/W2165743365","https://openalex.org/W1507318074","https://openalex.org/W4319653402","https://openalex.org/W2113160615","https://openalex.org/W2058277492","https://openalex.org/W2280308580","https://openalex.org/W2087516250","https://openalex.org/W2010357651","https://openalex.org/W3025200532"],"abstract_inverted_index":{"The":[0,33,62],"Lie":[1],"algebra":[2],"of":[3,11,35,56,64,77,93,108],"the":[4,38,53,59,74,85],"Lorentz":[5],"group":[6,107],"O(3,3)":[7],"admits":[8],"two":[9],"types":[10],"SU(2)":[12,14,80,82,101],"\u00d7":[13,81,102],"subalgebras:":[15],"a":[16,25,78,106],"standard":[17],"form":[18,27],"based":[19,28],"on":[20,29],"spatial":[21],"rotation":[22,31],"generators":[23],"and":[24,49,70,91],"second":[26],"temporal":[30,45,79],"generators.":[32],"units":[34,55],"measurement":[36],"for":[37],"conserved":[39],"quantity":[40],"due":[41],"to":[42,51,72,97],"invariance":[43],"under":[44],"rotations":[46],"are":[47,95,111],"investigated":[48],"found":[50,71,96],"be":[52,98],"same":[54],"measure":[57],"as":[58],"Planck":[60],"constant.":[61],"breaking":[63],"time":[65],"reversal":[66],"symmetry":[67,86],"is":[68,89],"considered":[69],"affect":[73],"chiral":[75],"properties":[76],"algebra.":[83],"Finally,":[84],"between":[87],"algebras":[88,94,110],"explored":[90],"pairs":[92],"related":[99,112],"by":[100,113],"U(1)":[103],"symmetry,":[104],"while":[105],"three":[109],"SO(4)":[114],"symmetry.":[115]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2020-05-21T00:00:00"}