On Orbits of 4-Dimensional Representations of 3-Dimensional Solvable Lie Algebras
In a 4-dimensional real space, we discuss linearly homogeneous hypersurfaces that are the orbits of 3-dimensional solvable Lie algebras. A complete list of inequivalent representations of a decomposable 3-dimensional algebra in space is given and a list of all (up to linear transformations) 3-dimens...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2023-04, Vol.44 (4), p.1383-1406 |
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| container_end_page | 1406 |
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| container_issue | 4 |
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| container_title | Lobachevskii journal of mathematics |
| container_volume | 44 |
| creator | Loboda, A. V. Akopyan, R. S. Darinskii, B. M. |
| description | In a 4-dimensional real space, we discuss linearly homogeneous hypersurfaces that are the orbits of 3-dimensional solvable Lie algebras. A complete list of inequivalent representations of a decomposable 3-dimensional algebra in
space is given and a list of all (up to linear transformations) 3-dimensional orbits of such representations. Most of the resulting hypersurfaces have trivial affine stabilizers and are new in the problem of describing affinely homogeneous varieties. |
| doi_str_mv | 10.1134/S1995080223040170 |
| format | Article |
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| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2023-04, Vol.44 (4), p.1383-1406 |
| issn | 1995-0802 1818-9962 |
| language | eng |
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| subjects | Algebra Analysis Geometry Hyperspaces Lie groups Linear transformations Mathematical Logic and Foundations Mathematics Mathematics and Statistics Orbits Probability Theory and Stochastic Processes Representations |
| title | On Orbits of 4-Dimensional Representations of 3-Dimensional Solvable Lie Algebras |
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