{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T17:00:47Z","timestamp":1761930047976,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,2]],"date-time":"2019-11-02T00:00:00Z","timestamp":1572652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras     A  5 , 7   a b c      to     A 18 a    . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.<\/jats:p>","DOI":"10.3390\/sym11111354","type":"journal-article","created":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T04:13:08Z","timestamp":1572840788000},"page":"1354","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5024-866X","authenticated-orcid":false,"given":"Hassan","family":"Almusawa","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA"},{"name":"Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia"}]},{"given":"Ryad","family":"Ghanam","sequence":"additional","affiliation":[{"name":"Department of Liberal Arts &amp; Sciences, Virginia Commonwealth University in Qatar, Doha 8095, Qatar"}]},{"given":"Gerard","family":"Thompson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Toledo, Toledo, OH 43606, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,2]]},"reference":[{"key":"ref_1","unstructured":"Olver, P.J. 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Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1354\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:31:22Z","timestamp":1760189482000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1354"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,2]]},"references-count":23,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["sym11111354"],"URL":"https:\/\/doi.org\/10.3390\/sym11111354","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,11,2]]}}}