1. ON THE DISCRETE SUBGROUPS AND HOMOGENEOUS SPACES OF NILPOTENT LIE GROUPS
- Author
-
Yozô Matsushima
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,Simple Lie group ,010102 general mathematics ,Lie group ,20.0X ,Central series ,01 natural sciences ,Representation theory ,Algebra ,Nilpotent ,Representation of a Lie group ,0103 physical sciences ,Lie theory ,0101 mathematics ,Nilpotent group ,Mathematics - Abstract
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.
- Published
- 1992