Abstract
Let Lo be the isotropy group of the origin in a semisimple flat homogeneous space M=L/Lo associated with a semisimple graded transitive Lie algebra l = g−1⊕g0⊕g1. It is a well known fact, due to T. Ochiai, that Lo can be considered as a Lie subgroup of G2(m), the Lie group of 2-jets j 20 (g) at 0 ∈ g−1, where g is a diffeomorphism from a neighbourhood of 0 ∈ g−1 ≡ R m onto a neighbourhood of 0 ∈g−1. The aim of this note is to show that Lo is in fact a closed subgroup when it has only a finite number of connected components, giving an affirmative answer to a conjecture suggested to us by M. Takeuchi one year ago.
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© 1984 Springer-Verlag
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Lopera, J.F.T. (1984). A note on semisimple flat homogeneous spaces. In: Naveira, A.M. (eds) Differential Geometry. Lecture Notes in Mathematics, vol 1045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072171
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DOI: https://doi.org/10.1007/BFb0072171
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