Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program
We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these...
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2022-08-01
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| Series: | Armenian Journal of Mathematics |
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| Online Access: | http://armjmath.sci.am/index.php/ajm/article/view/659 |
| _version_ | 1797947654691356672 |
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| author | Debapriya Biswas Ipsita Rajwar |
| author_facet | Debapriya Biswas Ipsita Rajwar |
| author_sort | Debapriya Biswas |
| collection | DOAJ |
| description |
We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.
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| first_indexed | 2024-04-10T21:30:11Z |
| format | Article |
| id | doaj.art-0f028b48ab914063b408e8fc50bd1b68 |
| institution | Directory Open Access Journal |
| issn | 1829-1163 |
| language | English |
| last_indexed | 2024-04-10T21:30:11Z |
| publishDate | 2022-08-01 |
| publisher | Republic of Armenia National Academy of Sciences |
| record_format | Article |
| series | Armenian Journal of Mathematics |
| spelling | doaj.art-0f028b48ab914063b408e8fc50bd1b682023-01-19T13:35:42ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632022-08-01141110.52737/18291163-2022.14.11-1-15Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen programDebapriya Biswas0Ipsita Rajwar1Indian Institute of Technology KharagpurIndian Institute of Technology Kharagpur We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points. http://armjmath.sci.am/index.php/ajm/article/view/659Lie Group $\text{SL}(3,\mathbb{R})$Homogeneous SpaceIwasawa DecompositionOne-Parameter SubgroupsGroup ActionDerived Representation |
| spellingShingle | Debapriya Biswas Ipsita Rajwar Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program Armenian Journal of Mathematics Lie Group $\text{SL}(3,\mathbb{R})$ Homogeneous Space Iwasawa Decomposition One-Parameter Subgroups Group Action Derived Representation |
| title | Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program |
| title_full | Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program |
| title_fullStr | Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program |
| title_full_unstemmed | Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program |
| title_short | Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program |
| title_sort | geometry associated with the text sl 3 mathbb r action on homogeneous space using the erlangen program |
| topic | Lie Group $\text{SL}(3,\mathbb{R})$ Homogeneous Space Iwasawa Decomposition One-Parameter Subgroups Group Action Derived Representation |
| url | http://armjmath.sci.am/index.php/ajm/article/view/659 |
| work_keys_str_mv | AT debapriyabiswas geometryassociatedwiththetextsl3mathbbractiononhomogeneousspaceusingtheerlangenprogram AT ipsitarajwar geometryassociatedwiththetextsl3mathbbractiononhomogeneousspaceusingtheerlangenprogram |