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On the Discrete Subgroups and Homogeneous Spaces of Nilpotent Lie Groups

Published online by Cambridge University Press:  22 January 2016

Yozô Matsushima
Yozô Matsushima*
Affiliation:
Mathematical Institute, Nagoya University
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Recently A, Malcev has shown that the homogeneous space of a connected nilpotent Lie group G is the direct product of a compact space and an Euclidean-space and that the compact space of this direct decomposition is also a homogeneous space of a connected subgroup of G. Any compact homogeneous space M of a connected nilpotent Lie group is of the form where is a connected simply connected nilpotent group whose structure constants are rational numbers in a suitable coordinate system and D is a discrete subgroup of G.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 2 , February 1951 , pp. 95 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

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