| Title:
|
Projective reparametrization of homogeneous curves (English) |
| Author:
|
Doubrov, Boris |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
129-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the conditions when locally homogeneous curves in homogeneous spaces admit a natural projective parameter. In particular, we prove that this is always the case for trajectories of homogeneous nilpotent elements in parabolic spaces. On algebraic level this corresponds to the generalization of Morozov–Jacobson theorem to graded semisimple Lie algebras. (English) |
| Keyword:
|
homogeneous submanifold |
| Keyword:
|
symmetry algebra |
| Keyword:
|
nilpotent elements |
| Keyword:
|
$sl_2$-tripple |
| MSC:
|
17B20 |
| MSC:
|
17B70 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1122.53029 |
| idMR:
|
MR2142149 |
| . |
| Date available:
|
2008-06-06T22:45:26Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107941 |
| . |
| Reference:
|
[1] Bourbaki N.: Éléments de mathématique, Fasc. XXXVIII: Groupes et algèbres de Lie. Chap. VII: Sous-algèbres de Cartan, éléments réguliers. Chap. VIII: Algèbres de Lie semi-simples déployées.Actualités scientifiques et industrielles, 1364, Paris, Hermann 1975. Zbl 0329.17002, MR 0453824 |
| Reference:
|
[2] Cap A., Slovák J., Žádník V.: On distinguished curves in parabolic geometries.Transform. Groups 9 (2004), 143–166. Zbl 1070.53021, MR 2056534 |
| Reference:
|
[3] Doubrov B., Komrakov B., Rabinovich M.: Homogeneous surfaces in three-dimensional affine geometry.In: Geometry and topology of submanifolds, VIII, Singapore, World Scientific 1996, 168–178. MR 1434565 |
| Reference:
|
[4] Doubrov B., Komrakov B.: Classification of homogeneous submanifolds in homogeneous spaces.Lobachevskii Journal of Mathematics 3 (1999), 19–38. Zbl 0964.53035, MR 1743130 |
| Reference:
|
[5] Eastwood M., Slovák J.: Preferred parametrizations on homogeneous curves.arXiv: math.DG/0311456. |
| Reference:
|
[6] Hermann R.: Sophus Lie’s 1880 transformation group paper.Math. Sci. Press Brookline 1975. Zbl 0406.22006, MR 0460053 |
| Reference:
|
[7] Jacobson N.: Lie algebras.Intersci. Tracts in Pure and Appl. Math. 10, New-York–London, John Wiley and Sons 1962. Zbl 0121.27504, MR 0143793 |
| Reference:
|
[8] Lie S.: Theorie der Transformationgruppen.Bd. 3, Leipzig, Teubner, 1893. |
| Reference:
|
[9] Vinberg E.: Classification of homogeneous nilpotent elements of a semisimple graded Lie algebra.Sel. Math. Sov. 6 (1987), 15–35. Zbl 0612.17010 |
| . |
