{"id":"https://openalex.org/W2982757629","doi":"https://doi.org/10.3390/sym11111354","title":"Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras","display_name":"Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras","publication_year":2019,"publication_date":"2019-11-02","ids":{"openalex":"https://openalex.org/W2982757629","doi":"https://doi.org/10.3390/sym11111354","mag":"2982757629"},"language":"en","primary_location":{"id":"doi:10.3390/sym11111354","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111354","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1354/pdf?version=1573805623","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/2073-8994/11/11/1354/pdf?version=1573805623","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013954454","display_name":"Hassan Almusawa","orcid":"https://orcid.org/0000-0001-5024-866X"},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]},{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA","US"],"is_corresponding":true,"raw_author_name":"Hassan Almusawa","raw_affiliation_strings":["Department of Mathematics &amp; Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA","Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5024-866X","affiliations":[{"raw_affiliation_string":"Department of Mathematics &amp; Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA","institution_ids":["https://openalex.org/I184840846"]},{"raw_affiliation_string":"Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070608993","display_name":"Ryad Ghanam","orcid":"https://orcid.org/0000-0003-3874-7567"},"institutions":[{"id":"https://openalex.org/I4210093164","display_name":"VCUQatar","ror":"https://ror.org/00k6x1e94","country_code":"QA","type":"education","lineage":["https://openalex.org/I184840846","https://openalex.org/I4210093164"]}],"countries":["QA"],"is_corresponding":false,"raw_author_name":"Ryad Ghanam","raw_affiliation_strings":["Department of Liberal Arts &amp; Sciences, Virginia Commonwealth University in Qatar, Doha 8095, Qatar"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Liberal Arts &amp; Sciences, Virginia Commonwealth University in Qatar, Doha 8095, Qatar","institution_ids":["https://openalex.org/I4210093164"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047620379","display_name":"Gerard Thompson","orcid":"https://orcid.org/0000-0003-1256-4500"},"institutions":[{"id":"https://openalex.org/I90871651","display_name":"University of Toledo","ror":"https://ror.org/01pbdzh19","country_code":"US","type":"education","lineage":["https://openalex.org/I90871651"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gerard Thompson","raw_affiliation_strings":["Department of Mathematics, University of Toledo, Toledo, OH 43606, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toledo, Toledo, OH 43606, USA","institution_ids":["https://openalex.org/I90871651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013954454"],"corresponding_institution_ids":["https://openalex.org/I184840846","https://openalex.org/I91450128"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5763,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66860899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"11","first_page":"1354","last_page":"1354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9976999759674072,"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":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lie-conformal-algebra","display_name":"Lie conformal algebra","score":0.6923887729644775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6761146783828735},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.6388684511184692},{"id":"https://openalex.org/keywords/adjoint-representation-of-a-lie-algebra","display_name":"Adjoint representation of a Lie algebra","score":0.5796843767166138},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5783844590187073},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5640309453010559},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5606834888458252},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.4998960494995117},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46476683020591736},{"id":"https://openalex.org/keywords/killing-form","display_name":"Killing form","score":0.4553641676902771},{"id":"https://openalex.org/keywords/graded-lie-algebra","display_name":"Graded Lie algebra","score":0.4515770971775055},{"id":"https://openalex.org/keywords/affine-lie-algebra","display_name":"Affine Lie algebra","score":0.4251961410045624},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.41818588972091675},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41071659326553345},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4065202474594116},{"id":"https://openalex.org/keywords/current-algebra","display_name":"Current algebra","score":0.18885985016822815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1694413125514984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07917028665542603}],"concepts":[{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.6923887729644775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6761146783828735},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6388684511184692},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.5796843767166138},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5783844590187073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5640309453010559},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5606834888458252},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.4998960494995117},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46476683020591736},{"id":"https://openalex.org/C99634282","wikidata":"https://www.wikidata.org/wiki/Q634557","display_name":"Killing form","level":5,"score":0.4553641676902771},{"id":"https://openalex.org/C144091092","wikidata":"https://www.wikidata.org/wiki/Q3611543","display_name":"Graded Lie algebra","level":3,"score":0.4515770971775055},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.4251961410045624},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.41818588972091675},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41071659326553345},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4065202474594116},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.18885985016822815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1694413125514984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07917028665542603}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym11111354","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111354","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1354/pdf?version=1573805623","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:scholarscompass.vcu.edu:math_pubs-1029","is_oa":true,"landing_page_url":"https://scholarscompass.vcu.edu/math_pubs/25","pdf_url":null,"source":{"id":"https://openalex.org/S4377196340","display_name":"VCU Scholars Compass (Virginia Commonwealth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184840846","host_organization_name":"Virginia Commonwealth University","host_organization_lineage":["https://openalex.org/I184840846"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Applied Mathematics Publications","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:3e161d8e5ddc4005a97d1cd35cb43842","is_oa":true,"landing_page_url":"https://doaj.org/article/3e161d8e5ddc4005a97d1cd35cb43842","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 11, Iss 11, p 1354 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/11/1354/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11111354","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11111354","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111354","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1354/pdf?version=1573805623","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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.44999998807907104}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311096","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79"},{"id":"https://openalex.org/F4320311223","display_name":"Jazan University","ror":"https://ror.org/02bjnq803"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2982757629.pdf","grobid_xml":"https://content.openalex.org/works/W2982757629.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W329282471","https://openalex.org/W592099572","https://openalex.org/W1566372820","https://openalex.org/W1969723685","https://openalex.org/W1999101721","https://openalex.org/W2008141772","https://openalex.org/W2031756342","https://openalex.org/W2046189903","https://openalex.org/W2048864540","https://openalex.org/W2060915908","https://openalex.org/W2069185213","https://openalex.org/W2092652900","https://openalex.org/W2162806633","https://openalex.org/W2910337784","https://openalex.org/W2979382527","https://openalex.org/W2995725582","https://openalex.org/W4246618248","https://openalex.org/W6757731931","https://openalex.org/W6768679560","https://openalex.org/W6772224920"],"related_works":["https://openalex.org/W2002468545","https://openalex.org/W2022071853","https://openalex.org/W2373781965","https://openalex.org/W2064429752","https://openalex.org/W3148960415","https://openalex.org/W2091234513","https://openalex.org/W2086520830","https://openalex.org/W4241517087","https://openalex.org/W2359012694","https://openalex.org/W4396916064"],"abstract_inverted_index":{"In":[0],"this":[1],"investigation,":[2],"we":[3],"present":[4],"symmetry":[5,56],"algebras":[6,23],"of":[7,12,18,42,54],"the":[8,13,39,50,55,62],"canonical":[9],"geodesic":[10],"equations":[11],"indecomposable":[14],"solvable":[15],"Lie":[16,52],"groups":[17],"dimension":[19],"five,":[20],"confined":[21],"to":[22,31],"A":[24,32],"5":[25],",":[26],"7":[27],"a":[28,34,47],"b":[29],"c":[30],"18":[33],".":[35],"For":[36],"each":[37],"algebra,":[38],"related":[40],"system":[41],"geodesics":[43],"is":[44],"provided.":[45],"Moreover,":[46],"basis":[48],"for":[49],"associated":[51],"algebra":[53],"vector":[57],"fields,":[58],"as":[59,61],"well":[60],"corresponding":[63],"nonzero":[64],"brackets,":[65],"are":[66],"constructed":[67],"and":[68],"categorized.":[69]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
