Abstract
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.
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Submitted by M. M. Arslanov
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Popov, V. On closedness of stationary subgroup of affine transformations group. Lobachevskii J Math 38, 724–729 (2017). https://doi.org/10.1134/S1995080217040175
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DOI: https://doi.org/10.1134/S1995080217040175