Coadjoint Orbits of Lie Algebras and Cartan Class
We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit O(α) at the point α corresponds to the characteristic space associated with the left invariant form α, and its dimension is the even part of the Cartan class of α. We apply this r...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210073 |
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| Cite this: | Coadjoint Orbits of Lie Algebras and Cartan Class / M. Goze, E. Remm // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ. |
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Goze, M. Remm, E. 2025-12-02T09:39:43Z 2019 Coadjoint Orbits of Lie Algebras and Cartan Class / M. Goze, E. Remm // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B20; 17B30; 53D10; 53D05 arXiv: 1806.07553 https://nasplib.isofts.kiev.ua/handle/123456789/210073 https://doi.org/10.3842/SIGMA.2019.002 We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit O(α) at the point α corresponds to the characteristic space associated with the left invariant form α, and its dimension is the even part of the Cartan class of α. We apply this remark to determine Lie algebras such that all the nontrivial orbits (nonreduced to a point) have the same dimension, in particular when this dimension is 2 or 4. We also determine the Lie algebras of dimension 2n or 2n+1 having an orbit of dimension 2n. The authors would like to thank the referees for their kind advice and useful comments to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Coadjoint Orbits of Lie Algebras and Cartan Class Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Coadjoint Orbits of Lie Algebras and Cartan Class |
| spellingShingle |
Coadjoint Orbits of Lie Algebras and Cartan Class Goze, M. Remm, E. |
| title_short |
Coadjoint Orbits of Lie Algebras and Cartan Class |
| title_full |
Coadjoint Orbits of Lie Algebras and Cartan Class |
| title_fullStr |
Coadjoint Orbits of Lie Algebras and Cartan Class |
| title_full_unstemmed |
Coadjoint Orbits of Lie Algebras and Cartan Class |
| title_sort |
coadjoint orbits of lie algebras and cartan class |
| author |
Goze, M. Remm, E. |
| author_facet |
Goze, M. Remm, E. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit O(α) at the point α corresponds to the characteristic space associated with the left invariant form α, and its dimension is the even part of the Cartan class of α. We apply this remark to determine Lie algebras such that all the nontrivial orbits (nonreduced to a point) have the same dimension, in particular when this dimension is 2 or 4. We also determine the Lie algebras of dimension 2n or 2n+1 having an orbit of dimension 2n.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210073 |
| citation_txt |
Coadjoint Orbits of Lie Algebras and Cartan Class / M. Goze, E. Remm // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ. |
| work_keys_str_mv |
AT gozem coadjointorbitsofliealgebrasandcartanclass AT remme coadjointorbitsofliealgebrasandcartanclass |
| first_indexed |
2025-12-07T21:24:17Z |
| last_indexed |
2025-12-07T21:24:17Z |
| _version_ |
1850886227275808768 |