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Clifford–Klein form
In mathematics, a Clifford–Klein form is a double coset space
:Γ\''G''/''H'',
where ''G'' is a reductive Lie group, ''H'' a closed subgroup of ''G'', and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space ''G''/''H''. A suitable discrete subgroup Γ may or may not exist, for a given ''G'' and ''H''. If Γ exists, there is the question of whether Γ\''G''/''H'' can be taken to be a compact space, called a compact Clifford–Klein form.
When ''H'' is itself compact, classical results show that a compact Clifford–Klein form exists. Otherwise it may not, and there are a number of negative results.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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