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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210073 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
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| ISSN: | 1815-0659 |