Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras
In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>A</mi> <mrow&g...
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MDPI AG
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/11/1354 |
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doaj-3e161d8e5ddc4005a97d1cd35cb438422020-11-25T02:03:10ZengMDPI AGSymmetry2073-89942019-11-011111135410.3390/sym11111354sym11111354Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie AlgebrasHassan Almusawa0Ryad Ghanam1Gerard Thompson2Department of Mathematics & Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USADepartment of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, Doha 8095, QatarDepartment of Mathematics, University of Toledo, Toledo, OH 43606, USAIn this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>A</mi> <mrow> <mn>5</mn> <mo>,</mo> <mn>7</mn> </mrow> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msubsup> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>A</mi> <mn>18</mn> <mi>a</mi> </msubsup> </semantics> </math> </inline-formula>. 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.https://www.mdpi.com/2073-8994/11/11/1354symmetry algebralie groupcanonical connectionsystem of geodesic equations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hassan Almusawa Ryad Ghanam Gerard Thompson |
| spellingShingle |
Hassan Almusawa Ryad Ghanam Gerard Thompson Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras Symmetry symmetry algebra lie group canonical connection system of geodesic equations |
| author_facet |
Hassan Almusawa Ryad Ghanam Gerard Thompson |
| author_sort |
Hassan Almusawa |
| title |
Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras |
| title_short |
Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras |
| title_full |
Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras |
| title_fullStr |
Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras |
| title_full_unstemmed |
Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras |
| title_sort |
classification of symmetry lie algebras of the canonical geodesic equations of five-dimensional solvable lie algebras |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2019-11-01 |
| description |
In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>A</mi> <mrow> <mn>5</mn> <mo>,</mo> <mn>7</mn> </mrow> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msubsup> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>A</mi> <mn>18</mn> <mi>a</mi> </msubsup> </semantics> </math> </inline-formula>. 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. |
| topic |
symmetry algebra lie group canonical connection system of geodesic equations |
| url |
https://www.mdpi.com/2073-8994/11/11/1354 |
| work_keys_str_mv |
AT hassanalmusawa classificationofsymmetryliealgebrasofthecanonicalgeodesicequationsoffivedimensionalsolvableliealgebras AT ryadghanam classificationofsymmetryliealgebrasofthecanonicalgeodesicequationsoffivedimensionalsolvableliealgebras AT gerardthompson classificationofsymmetryliealgebrasofthecanonicalgeodesicequationsoffivedimensionalsolvableliealgebras |
| _version_ |
1724949052870623232 |