On closedness of stationary subgroup of affine transformations group
- Autores: Popov V.1
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Afiliações:
- Financial University under the Government of Russian Federation
- Edição: Volume 38, Nº 4 (2017)
- Páginas: 724-729
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199699
- DOI: https://doi.org/10.1134/S1995080217040175
- ID: 199699
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Resumo
This article deals with Lie algebra g of all infinitesimal affine transformations on a manifold with affine connection and its stationary subalgebra h ⊂ g. Let G be simply connected group generated by algebra g and H ⊂ G be the subgroup generated by subalgebra h ⊂ g and let dimg/h = dimM. Then if algebra g has zero center the subgroup H is closed in G. Thus any infinitesimal affine transformation X ⊂ g on a manifold M = G/H can be extended to affine transformation f: M → M. For Riemannian manifolds the condition dimg/h = dimM can be omitted and the main result can be generalized for algebra g with non-zero center.
Sobre autores
V. Popov
Financial University under the Government of Russian Federation
Autor responsável pela correspondência
Email: vlapopov@gmail.com
Rússia, Leninskii pr. 49, Moscow, 125093